n-2*180/n=180

Solution for n-2*180/n=180 equation:

n-2*180/n=180

We move all terms to the left:

n-2*180/n-(180)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


n*n-180*n-2*180=0

We add all the numbers together, and all the variables

-180n+n*n-360=0

Wy multiply elements

n^2-180n-360=0

a = 1; b = -180; c = -360;
Δ = b2-4ac
Δ = -1802-4·1·(-360)
Δ = 33840
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:

$\sqrt{\Delta}=\sqrt{33840}=\sqrt{144*235}=\sqrt{144}*\sqrt{235}=12\sqrt{235}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-12\sqrt{235}}{2*1}=\frac{180-12\sqrt{235}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+12\sqrt{235}}{2*1}=\frac{180+12\sqrt{235}}{2}
$