180n-360/n=120

Solution for 180n-360/n=120 equation:

180n-360/n=120

We move all terms to the left:

180n-360/n-(120)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


180n*n-120*n-360=0

We add all the numbers together, and all the variables

-120n+180n*n-360=0

Wy multiply elements

180n^2-120n-360=0

a = 180; b = -120; c = -360;
Δ = b2-4ac
Δ = -1202-4·180·(-360)
Δ = 273600
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:

$\sqrt{\Delta}=\sqrt{273600}=\sqrt{14400*19}=\sqrt{14400}*\sqrt{19}=120\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120\sqrt{19}}{2*180}=\frac{120-120\sqrt{19}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120\sqrt{19}}{2*180}=\frac{120+120\sqrt{19}}{360}
$