Help deriving the cubic equation

[MC Master of Ceremonies]

Now I'm not, asking for the proof or even the cubic equation, I would just like a few pointers on the methods used to derive the cubic equation.

[Desmostylus]

http://mathworld.wolfram.com/CubicEquation.html

Read, don't read it, whatever.

[MC Master of Ceremonies]

'tis more complex than I thought. I thought there would be one general, if not long equation to solve for all of it, quickly looking at the link their seems to be different equations to solve for different parts.

[Shade]

I think there might be a general equation, but it's a lot less convenient than this.

Why don't you try and find the equation for a quintic?

That was a joke.

[raygirvan]

They're just breaking it down for ease of vertical presentation. It boils down to: with suitable substitutions, the original cubic can be expressed as a quadratic, one of whose solutions is a quadratic in itself. This page (http://people.ucsc.edu/~erowland/polynomials.html) gives a somewhat terser sketch of the process.