How do you solve a cubic?

Answer 1

Although there are formal methods, the simplest is to see if the cubic can be factorised. If so, you'll have a linear factor and a quadratic, both of which are easy to solve.

Alternatively, you could try solving it graphically.

Another possibility is to solve it numerically. The derivative of a cubic, of the form f(x) = ax3 + bx2 + cx + d is f'(x) = 3ax2 + 2bx + c.

Make an initial estimate x1. An improved estimate is x2 = x1 - f(x1)/f'(x1). Use x2 to make next estimate, and so on.