180n-360=2880/8n

Solution for 180n-360=2880/8n equation:

180n-360=2880/8n

We move all terms to the left:

180n-360-(2880/8n)=0


Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

180n-(+2880/8n)-360=0

We get rid of parentheses

180n-2880/8n-360=0

We multiply all the terms by the denominator


180n*8n-360*8n-2880=0

Wy multiply elements

1440n^2-2880n-2880=0

a = 1440; b = -2880; c = -2880;
Δ = b2-4ac
Δ = -28802-4·1440·(-2880)
Δ = 24883200
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:

$\sqrt{\Delta}=\sqrt{24883200}=\sqrt{8294400*3}=\sqrt{8294400}*\sqrt{3}=2880\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2880)-2880\sqrt{3}}{2*1440}=\frac{2880-2880\sqrt{3}}{2880}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2880)+2880\sqrt{3}}{2*1440}=\frac{2880+2880\sqrt{3}}{2880}
$