180n-360/n=156

Solution for 180n-360/n=156 equation:

180n-360/n=156

We move all terms to the left:

180n-360/n-(156)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


180n*n-156*n-360=0

We add all the numbers together, and all the variables

-156n+180n*n-360=0

Wy multiply elements

180n^2-156n-360=0

a = 180; b = -156; c = -360;
Δ = b2-4ac
Δ = -1562-4·180·(-360)
Δ = 283536
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:

$\sqrt{\Delta}=\sqrt{283536}=\sqrt{144*1969}=\sqrt{144}*\sqrt{1969}=12\sqrt{1969}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-12\sqrt{1969}}{2*180}=\frac{156-12\sqrt{1969}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+12\sqrt{1969}}{2*180}=\frac{156+12\sqrt{1969}}{360}
$