5n(4n-16)=180

Solution for 5n(4n-16)=180 equation:

5n(4n-16)=180

We move all terms to the left:

5n(4n-16)-(180)=0

We multiply parentheses

20n^2-80n-180=0

a = 20; b = -80; c = -180;
Δ = b2-4ac
Δ = -802-4·20·(-180)
Δ = 20800
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:

$\sqrt{\Delta}=\sqrt{20800}=\sqrt{1600*13}=\sqrt{1600}*\sqrt{13}=40\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{13}}{2*20}=\frac{80-40\sqrt{13}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{13}}{2*20}=\frac{80+40\sqrt{13}}{40}
$