Are you looking to find the roots of a third degree polynomial with a numerical method?
Well, i came across some equations in thermodynamics that was solved with this method it seemed eaiser and faster but i couldnt figure it out on my own. they actually showed us about it in calculus ii last year but i didnt pay much attention since i didnt need it untill now. theres no particular polynominal, feel free to give a simple example.
Well as you studied calculus I would suggest using newton's method. It is an iterative process.
You keep calculating the next value until you see convergence. This value will be the solution.
For the polynomial choose a starting value in the neighbourhood of the solution, in this case and apply
What did you get?
Note this value and find repeat