(x+120)(x+15)=180

Solution for (x+120)(x+15)=180 equation:

(x+120)(x+15)=180

We move all terms to the left:

(x+120)(x+15)-(180)=0

We multiply parentheses ..

(+x^2+15x+120x+1800)-180=0

We get rid of parentheses

x^2+15x+120x+1800-180=0

We add all the numbers together, and all the variables

x^2+135x+1620=0

a = 1; b = 135; c = +1620;
Δ = b2-4ac
Δ = 1352-4·1·1620
Δ = 11745
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:

$\sqrt{\Delta}=\sqrt{11745}=\sqrt{81*145}=\sqrt{81}*\sqrt{145}=9\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-9\sqrt{145}}{2*1}=\frac{-135-9\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+9\sqrt{145}}{2*1}=\frac{-135+9\sqrt{145}}{2}
$