How do we factor a quadratic equation?

[Miike012]

I added an attachment and highlited my question... basically I am confused how they got there.

 

[Zryn]

It's just a bit of rearranging:

Given y = $\sqrt{ax^{2} + bx + c}$

$y^{2}$ = a$x^{2}$ + bx + c.

So replace a$x^{2}$ + bx + c from the initial equation with $y^{2}$.

Replace the $\sqrt{ax^{2} + bx + c}$ part of the initial equation with y.

Move q from one side of the equation to the other.

Presto chango, $y^{2}$ + py - q = 0.