x^2+(x^2+6x+9)=225

Solution for x^2+(x^2+6x+9)=225 equation:

x^2+(x^2+6x+9)=225

We move all terms to the left:

x^2+(x^2+6x+9)-(225)=0

We get rid of parentheses

x^2+x^2+6x+9-225=0

We add all the numbers together, and all the variables

2x^2+6x-216=0

a = 2; b = 6; c = -216;
Δ = b2-4ac
Δ = 62-4·2·(-216)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-42}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+42}{2*2}=\frac{36}{4}
=9
$