180n-360/n=140

Solution for 180n-360/n=140 equation:

180n-360/n=140

We move all terms to the left:

180n-360/n-(140)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


180n*n-140*n-360=0

We add all the numbers together, and all the variables

-140n+180n*n-360=0

Wy multiply elements

180n^2-140n-360=0

a = 180; b = -140; c = -360;
Δ = b2-4ac
Δ = -1402-4·180·(-360)
Δ = 278800
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:

$\sqrt{\Delta}=\sqrt{278800}=\sqrt{400*697}=\sqrt{400}*\sqrt{697}=20\sqrt{697}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-20\sqrt{697}}{2*180}=\frac{140-20\sqrt{697}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+20\sqrt{697}}{2*180}=\frac{140+20\sqrt{697}}{360}
$