x(x+36)=180

Solution for x(x+36)=180 equation:

x(x+36)=180

We move all terms to the left:

x(x+36)-(180)=0

We multiply parentheses

x^2+36x-180=0

a = 1; b = 36; c = -180;
Δ = b2-4ac
Δ = 362-4·1·(-180)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{14}}{2*1}=\frac{-36-12\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{14}}{2*1}=\frac{-36+12\sqrt{14}}{2}
$