x(x+36)=120

Solution for x(x+36)=120 equation:

x(x+36)=120

We move all terms to the left:

x(x+36)-(120)=0

We multiply parentheses

x^2+36x-120=0

a = 1; b = 36; c = -120;
Δ = b2-4ac
Δ = 362-4·1·(-120)
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{111}}{2*1}=\frac{-36-4\sqrt{111}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{111}}{2*1}=\frac{-36+4\sqrt{111}}{2}
$