n(n+75)=180

Solution for n(n+75)=180 equation:

n(n+75)=180

We move all terms to the left:

n(n+75)-(180)=0

We multiply parentheses

n^2+75n-180=0

a = 1; b = 75; c = -180;
Δ = b2-4ac
Δ = 752-4·1·(-180)
Δ = 6345
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:

$\sqrt{\Delta}=\sqrt{6345}=\sqrt{9*705}=\sqrt{9}*\sqrt{705}=3\sqrt{705}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-3\sqrt{705}}{2*1}=\frac{-75-3\sqrt{705}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+3\sqrt{705}}{2*1}=\frac{-75+3\sqrt{705}}{2}
$