solve for x in x^3+x^2-a = 0

Input interpretation

solve x^3 + x^2 - a = 0 for x

Result

x = 1/3 ((3 sqrt(3) sqrt(27 a^2 - 4 a) + 27 a - 2)^(1/3)/2^(1/3) + 2^(1/3)/(3 sqrt(3) sqrt(27 a^2 - 4 a) + 27 a - 2)^(1/3) - 1)

x = -((1 - i sqrt(3)) (3 sqrt(3) sqrt(27 a^2 - 4 a) + 27 a - 2)^(1/3))/(6 2^(1/3)) - (1 + i sqrt(3))/(3 2^(2/3) (3 sqrt(3) sqrt(27 a^2 - 4 a) + 27 a - 2)^(1/3)) - 1/3

x = -((1 + i sqrt(3)) (3 sqrt(3) sqrt(27 a^2 - 4 a) + 27 a - 2)^(1/3))/(6 2^(1/3)) - (1 - i sqrt(3))/(3 2^(2/3) (3 sqrt(3) sqrt(27 a^2 - 4 a) + 27 a - 2)^(1/3)) - 1/3