Cubic root formula derivation I'm trying to understand the derivation for the cubic root formula. The text I am studying from describes the following steps:
$$x^3 + ax^2 + bx + c = 0$$
Reduce this to a depressed form by substituting $y = x + \frac{a}{3}$. Such that:
$$y^3 = (x + \frac{a}{3})^3 = x^3 + ax^2 + \frac{a^2}{3}x + \frac{a^3}{27}$$
So the cubic equation becomes $y^3 + b'y + c'=0$, which can then be written as $y^3 + 3hy + k = 0$. 
I understand that the aim is to remove the quadratic component, but where $b'$ and $c'$ are used I obviously lack some elementary knowledge. I feel like adding $b'y$ and $c'$ to $y^3$ modifies the last two terms, meaning they equate to $bx + c$, is that correct? 
I don't understand why $3h$ is chosen though, can anyone clarify?

If you replace $x$ in your original equation by $y-\frac{a}{3}$, you get:  


*

*$y^3+p\cdot y+q$  


with  


*

*$p=b-\frac{a^2}{3}$

*$q=\large\frac{2a^3}{27}\normalsize -\large\frac{ab}{3}\normalsize +c$


And for what? Now you are able to solve the new problem without a quadratic component by Cadano's method (bether: del Ferro-"Tartaglia"-Cardano method).
