n(n-5)=180

Solution for n(n-5)=180 equation:

n(n-5)=180

We move all terms to the left:

n(n-5)-(180)=0

We multiply parentheses

n^2-5n-180=0

a = 1; b = -5; c = -180;
Δ = b2-4ac
Δ = -52-4·1·(-180)
Δ = 745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{745}}{2*1}=\frac{5-\sqrt{745}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{745}}{2*1}=\frac{5+\sqrt{745}}{2}
$