n(n-2)*180=135

Solution for n(n-2)*180=135 equation:

n(n-2)*180=135

We move all terms to the left:

n(n-2)*180-(135)=0

We multiply parentheses

180n^2-360n-135=0

a = 180; b = -360; c = -135;
Δ = b2-4ac
Δ = -3602-4·180·(-135)
Δ = 226800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{226800}=\sqrt{32400*7}=\sqrt{32400}*\sqrt{7}=180\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-180\sqrt{7}}{2*180}=\frac{360-180\sqrt{7}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+180\sqrt{7}}{2*180}=\frac{360+180\sqrt{7}}{360}
$