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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2+15x+30x+225)-180=0

We get rid of parentheses

2x^2+15x+30x+225-180=0

We add all the numbers together, and all the variables

2x^2+45x+45=0

a = 2; b = 45; c = +45;
Δ = b2-4ac
Δ = 452-4·2·45
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{185}}{2*2}=\frac{-45-3\sqrt{185}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{185}}{2*2}=\frac{-45+3\sqrt{185}}{4}
$