180(n-2)n=9

Solution for 180(n-2)n=9 equation:

180(n-2)n=9

We move all terms to the left:

180(n-2)n-(9)=0

We multiply parentheses

180n^2-360n-9=0

a = 180; b = -360; c = -9;
Δ = b2-4ac
Δ = -3602-4·180·(-9)
Δ = 136080
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:

$\sqrt{\Delta}=\sqrt{136080}=\sqrt{1296*105}=\sqrt{1296}*\sqrt{105}=36\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-36\sqrt{105}}{2*180}=\frac{360-36\sqrt{105}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+36\sqrt{105}}{2*180}=\frac{360+36\sqrt{105}}{360}
$