一般解是复数形式. 基本过程如下:
ax^3+bx^2+cx+d=0 (1)
设x1 = x + b/(3a)
则
x1^3 + (c/a - (b/a)^2 / 3)x1 + d/a - (b/(3a))^3-b/(3a) (c/a - (b/a)^2 / 3) = 0;
设 p = -(c/a - (b/a)^2 / 3), q = -(d/a - (b/(3a))^3-b/(3a) (c/a - (b/a)^2 / 3)) , 则
x1^3 - p x1 - q = 0 (2)
设p = 3mn, q = m^3 + n^3, 则x1 = m+n
由p = 3mn, q=m^3 + n^3 计算出m 和 n的值, 去掉无效解, 保留3组m,n值,
即可解出x1, 从而解出x