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} = ax^{2} + bx + c.

So replace ax^{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.