n(n-2)=90

Solution for n(n-2)=90 equation:

n(n-2)=90

We move all terms to the left:

n(n-2)-(90)=0

We multiply parentheses

n^2-2n-90=0

a = 1; b = -2; c = -90;
Δ = b2-4ac
Δ = -22-4·1·(-90)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{91}}{2*1}=\frac{2-2\sqrt{91}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{91}}{2*1}=\frac{2+2\sqrt{91}}{2}
$