n-2*180/n=156

Solution for n-2*180/n=156 equation:

n-2*180/n=156

We move all terms to the left:

n-2*180/n-(156)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


n*n-156*n-2*180=0

We add all the numbers together, and all the variables

-156n+n*n-360=0

Wy multiply elements

n^2-156n-360=0

a = 1; b = -156; c = -360;
Δ = b2-4ac
Δ = -1562-4·1·(-360)
Δ = 25776
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:

$\sqrt{\Delta}=\sqrt{25776}=\sqrt{144*179}=\sqrt{144}*\sqrt{179}=12\sqrt{179}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-12\sqrt{179}}{2*1}=\frac{156-12\sqrt{179}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+12\sqrt{179}}{2*1}=\frac{156+12\sqrt{179}}{2}
$