45+(2x)(x+15)=180

Solution for 45+(2x)(x+15)=180 equation:

45+(2x)(x+15)=180

We move all terms to the left:

45+(2x)(x+15)-(180)=0

We add all the numbers together, and all the variables

2x(x+15)-135=0

We multiply parentheses

2x^2+30x-135=0

a = 2; b = 30; c = -135;
Δ = b2-4ac
Δ = 302-4·2·(-135)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{55}}{2*2}=\frac{-30-6\sqrt{55}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{55}}{2*2}=\frac{-30+6\sqrt{55}}{4}
$