(2x-15+x)(2x-15+x)=180

Solution for (2x-15+x)(2x-15+x)=180 equation:

(2x-15+x)(2x-15+x)=180

We move all terms to the left:

(2x-15+x)(2x-15+x)-(180)=0

We add all the numbers together, and all the variables

(3x-15)(3x-15)-180=0

We multiply parentheses ..

(+9x^2-45x-45x+225)-180=0

We get rid of parentheses

9x^2-45x-45x+225-180=0

We add all the numbers together, and all the variables

9x^2-90x+45=0

a = 9; b = -90; c = +45;
Δ = b2-4ac
Δ = -902-4·9·45
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-36\sqrt{5}}{2*9}=\frac{90-36\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+36\sqrt{5}}{2*9}=\frac{90+36\sqrt{5}}{18}
$