4n(5n+6)=180

Solution for 4n(5n+6)=180 equation:

4n(5n+6)=180

We move all terms to the left:

4n(5n+6)-(180)=0

We multiply parentheses

20n^2+24n-180=0

a = 20; b = 24; c = -180;
Δ = b2-4ac
Δ = 242-4·20·(-180)
Δ = 14976
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:

$\sqrt{\Delta}=\sqrt{14976}=\sqrt{576*26}=\sqrt{576}*\sqrt{26}=24\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{26}}{2*20}=\frac{-24-24\sqrt{26}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{26}}{2*20}=\frac{-24+24\sqrt{26}}{40}
$