2(n^2+n)=180

Solution for 2(n^2+n)=180 equation:

2(n^2+n)=180

We move all terms to the left:

2(n^2+n)-(180)=0

We multiply parentheses

2n^2+2n-180=0

a = 2; b = 2; c = -180;
Δ = b2-4ac
Δ = 22-4·2·(-180)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*2}=\frac{-40}{4}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*2}=\frac{36}{4}
=9
$