n-2/n*180=172

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

n-2/n*180=172

We move all terms to the left:

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


Domain of the equation: n*180!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


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

Wy multiply elements

180n^2*1-30960n*1-2=0

Wy multiply elements

180n^2-30960n-2=0

a = 180; b = -30960; c = -2;
Δ = b2-4ac
Δ = -309602-4·180·(-2)
Δ = 958523040
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:

$\sqrt{\Delta}=\sqrt{958523040}=\sqrt{144*6656410}=\sqrt{144}*\sqrt{6656410}=12\sqrt{6656410}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30960)-12\sqrt{6656410}}{2*180}=\frac{30960-12\sqrt{6656410}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30960)+12\sqrt{6656410}}{2*180}=\frac{30960+12\sqrt{6656410}}{360}
$