CoCalc -- 330.sagews

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x = var('x')

solve(5*x^4+(29/6-10/(3)^(1/3))*x^3-x-7/6+2/(3)^(1/3),x);

[x == -sqrt((1800*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (-841*3^(2/3) + 3480*3^(1/3) - 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 444*3^(2/3) + 720*3^(1/3))*sqrt(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3)) + (151380*3^(2/3) - 313200*3^(1/3) + 272433)*sqrt(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3))))*I/(60*sqrt(2)*3^(1/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/6)*(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3))^(1/4)) - sqrt(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3))/(120*3^(1/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/6)) + (60 - 29*3^(1/3))/(120*3^(1/3)), x == sqrt((1800*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (-841*3^(2/3) + 3480*3^(1/3) - 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 444*3^(2/3) + 720*3^(1/3))*sqrt(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3)) + (151380*3^(2/3) - 313200*3^(1/3) + 272433)*sqrt(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3))))*I/(60*sqrt(2)*3^(1/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/6)*(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3))^(1/4)) - sqrt(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3))/(120*3^(1/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/6)) + (60 - 29*3^(1/3))/(120*3^(1/3)), x == -sqrt((-1800*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) - (-841*3^(2/3) + 3480*3^(1/3) - 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) + 444*3^(2/3) - 720*3^(1/3))*sqrt(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3)) - (-151380*3^(2/3) + 313200*3^(1/3) - 272433)*sqrt(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3))))/(60*sqrt(2)*3^(1/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/6)*(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3))^(1/4)) + sqrt(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3))/(120*3^(1/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/6)) + (60 - 29*3^(1/3))/(120*3^(1/3)), x == sqrt((-1800*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) - (-841*3^(2/3) + 3480*3^(1/3) - 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) + 444*3^(2/3) - 720*3^(1/3))*sqrt(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3)) - (-151380*3^(2/3) + 313200*3^(1/3) - 272433)*sqrt(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3))))/(60*sqrt(2)*3^(1/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/6)*(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3))^(1/4)) + sqrt(3600*3^(2/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(2/3) + (841*3^(2/3) - 3480*3^(1/3) + 3600)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/3) - 888*3^(2/3) + 1440*3^(1/3))/(120*3^(1/3)*(sqrt(-1464355439*3^(2/3) + 1942636392*3^(1/3) + 247500144)/(54000*3^(1/3)) - (22320*3^(2/3) - 9593*3^(1/3) - 34452)/(54000*3^(1/3)))^(1/6)) + (60 - 29*3^(1/3))/(120*3^(1/3))]