N(n^2-1)=180

Solution for N(n^2-1)=180 equation:

(N^2-1)=180

We move all terms to the left:

(N^2-1)-(180)=0

We get rid of parentheses

N^2-1-180=0

We add all the numbers together, and all the variables

N^2-181=0

a = 1; b = 0; c = -181;
Δ = b2-4ac
Δ = 02-4·1·(-181)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{181}}{2*1}=\frac{0-2\sqrt{181}}{2}
=-\frac{2\sqrt{181}}{2}
=-\sqrt{181}
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{181}}{2*1}=\frac{0+2\sqrt{181}}{2}
=\frac{2\sqrt{181}}{2}
=\sqrt{181}
$