(8n+8)(9n)=180

Solution for (8n+8)(9n)=180 equation:

(8n+8)(9n)=180

We move all terms to the left:

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

We multiply parentheses

72n^2+72n-180=0

a = 72; b = 72; c = -180;
Δ = b2-4ac
Δ = 722-4·72·(-180)
Δ = 57024
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:

$\sqrt{\Delta}=\sqrt{57024}=\sqrt{5184*11}=\sqrt{5184}*\sqrt{11}=72\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72\sqrt{11}}{2*72}=\frac{-72-72\sqrt{11}}{144}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72\sqrt{11}}{2*72}=\frac{-72+72\sqrt{11}}{144}
$