8n(9n-5)=180

Solution for 8n(9n-5)=180 equation:

8n(9n-5)=180

We move all terms to the left:

8n(9n-5)-(180)=0

We multiply parentheses

72n^2-40n-180=0

a = 72; b = -40; c = -180;
Δ = b2-4ac
Δ = -402-4·72·(-180)
Δ = 53440
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:

$\sqrt{\Delta}=\sqrt{53440}=\sqrt{64*835}=\sqrt{64}*\sqrt{835}=8\sqrt{835}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{835}}{2*72}=\frac{40-8\sqrt{835}}{144}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{835}}{2*72}=\frac{40+8\sqrt{835}}{144}
$