x(x-180)=180

Solution for x(x-180)=180 equation:

x(x-180)=180

We move all terms to the left:

x(x-180)-(180)=0

We multiply parentheses

x^2-180x-180=0

a = 1; b = -180; c = -180;
Δ = b2-4ac
Δ = -1802-4·1·(-180)
Δ = 33120
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:

$\sqrt{\Delta}=\sqrt{33120}=\sqrt{144*230}=\sqrt{144}*\sqrt{230}=12\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-12\sqrt{230}}{2*1}=\frac{180-12\sqrt{230}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+12\sqrt{230}}{2*1}=\frac{180+12\sqrt{230}}{2}
$