0=x^2-9x-252

Solution for 0=x^2-9x-252 equation:

0=x^2-9x-252

We move all terms to the left:

0-(x^2-9x-252)=0

We add all the numbers together, and all the variables

-(x^2-9x-252)=0

We get rid of parentheses

-x^2+9x+252=0

We add all the numbers together, and all the variables

-1x^2+9x+252=0

a = -1; b = 9; c = +252;
Δ = b2-4ac
Δ = 92-4·(-1)·252
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-33}{2*-1}=\frac{-42}{-2}
=+21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+33}{2*-1}=\frac{24}{-2}
=-12
$