180n^2=540+360n

Solution for 180n^2=540+360n equation:

180n^2=540+360n

We move all terms to the left:

180n^2-(540+360n)=0

We add all the numbers together, and all the variables

180n^2-(360n+540)=0

We get rid of parentheses

180n^2-360n-540=0

a = 180; b = -360; c = -540;
Δ = b2-4ac
Δ = -3602-4·180·(-540)
Δ = 518400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{518400}=720$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-720}{2*180}=\frac{-360}{360}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+720}{2*180}=\frac{1080}{360}
=3
$