n-2*180/n=172

Solution for n-2*180/n=172 equation:

n-2*180/n=172

We move all terms to the left:

n-2*180/n-(172)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


n*n-172*n-2*180=0

We add all the numbers together, and all the variables

-172n+n*n-360=0

Wy multiply elements

n^2-172n-360=0

a = 1; b = -172; c = -360;
Δ = b2-4ac
Δ = -1722-4·1·(-360)
Δ = 31024
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:

$\sqrt{\Delta}=\sqrt{31024}=\sqrt{16*1939}=\sqrt{16}*\sqrt{1939}=4\sqrt{1939}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-4\sqrt{1939}}{2*1}=\frac{172-4\sqrt{1939}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+4\sqrt{1939}}{2*1}=\frac{172+4\sqrt{1939}}{2}
$