n(n-60)=180

Solution for n(n-60)=180 equation:

n(n-60)=180

We move all terms to the left:

n(n-60)-(180)=0

We multiply parentheses

n^2-60n-180=0

a = 1; b = -60; c = -180;
Δ = b2-4ac
Δ = -602-4·1·(-180)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{30}}{2*1}=\frac{60-12\sqrt{30}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{30}}{2*1}=\frac{60+12\sqrt{30}}{2}
$