0=x^2+12x-225

Solution for 0=x^2+12x-225 equation:

0=x^2+12x-225

We move all terms to the left:

0-(x^2+12x-225)=0

We add all the numbers together, and all the variables

-(x^2+12x-225)=0

We get rid of parentheses

-x^2-12x+225=0

We add all the numbers together, and all the variables

-1x^2-12x+225=0

a = -1; b = -12; c = +225;
Δ = b2-4ac
Δ = -122-4·(-1)·225
Δ = 1044
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{29}}{2*-1}=\frac{12-6\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{29}}{2*-1}=\frac{12+6\sqrt{29}}{-2}
$