180n-540=2880/n

Solution for 180n-540=2880/n equation:

180n-540=2880/n

We move all terms to the left:

180n-540-(2880/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

180n-(+2880/n)-540=0

We get rid of parentheses

180n-2880/n-540=0

We multiply all the terms by the denominator


180n*n-540*n-2880=0

We add all the numbers together, and all the variables

-540n+180n*n-2880=0

Wy multiply elements

180n^2-540n-2880=0

a = 180; b = -540; c = -2880;
Δ = b2-4ac
Δ = -5402-4·180·(-2880)
Δ = 2365200
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:

$\sqrt{\Delta}=\sqrt{2365200}=\sqrt{32400*73}=\sqrt{32400}*\sqrt{73}=180\sqrt{73}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-180\sqrt{73}}{2*180}=\frac{540-180\sqrt{73}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+180\sqrt{73}}{2*180}=\frac{540+180\sqrt{73}}{360}
$