(n-2)180=2(360)/n

Solution for (n-2)180=2(360)/n equation:

(n-2)180=2(360)/n

We move all terms to the left:

(n-2)180-(2(360)/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

(n-2)180-(+2360/n)=0

We multiply parentheses

180n-(+2360/n)-360=0

We get rid of parentheses

180n-2360/n-360=0

We multiply all the terms by the denominator


180n*n-360*n-2360=0

We add all the numbers together, and all the variables

-360n+180n*n-2360=0

Wy multiply elements

180n^2-360n-2360=0

a = 180; b = -360; c = -2360;
Δ = b2-4ac
Δ = -3602-4·180·(-2360)
Δ = 1828800
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:

$\sqrt{\Delta}=\sqrt{1828800}=\sqrt{14400*127}=\sqrt{14400}*\sqrt{127}=120\sqrt{127}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-120\sqrt{127}}{2*180}=\frac{360-120\sqrt{127}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+120\sqrt{127}}{2*180}=\frac{360+120\sqrt{127}}{360}
$