Using completing the square method we can derive a formula $ax^2+bx+c=0$ for the quadratic equation to $$x={-b\pm \sqrt{b^2-4ac}\over 2a}$$
I am sure I haven't sees it in any book talking about deriving the cubic equation $ax^3+bx^2+cx+d=0$ using the method of completing the square or the cube.
So how did they derive the cubic formula to solve the cubic equation?