What is the formula to solve a cubic equation?

Question

I know that to solve $$ax^2+bx+c=0$$

you have to use the formula $$x= \frac{-b \pm \sqrt{(b^2-4ac)}}{2a}$$

What about more complex ones, like $ax^3+bx^2+cx+d=0$? And what about representing it on a cordinate plane, $2D$ or $3D$?

Answer 1

There are ways to solve polynomial equations up to degree 4 in terms of radicals. For example, to solve a cubic equation, have a look here:

https://en.wikipedia.org/wiki/Cubic_function#General_solution_to_the_cubic_equation_with_real_coefficients

There is no general algebraic formula to solve a polynomial equation that has degree 5 or higher in terms only of radicals.