(x+15)(x+15)=54

Solution for (x+15)(x+15)=54 equation:

(x+15)(x+15)=54

We move all terms to the left:

(x+15)(x+15)-(54)=0

We multiply parentheses ..

(+x^2+15x+15x+225)-54=0

We get rid of parentheses

x^2+15x+15x+225-54=0

We add all the numbers together, and all the variables

x^2+30x+171=0

a = 1; b = 30; c = +171;
Δ = b2-4ac
Δ = 302-4·1·171
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{6}}{2*1}=\frac{-30-6\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{6}}{2*1}=\frac{-30+6\sqrt{6}}{2}
$