120=180n-360/n

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

120=180n-360/n

We move all terms to the left:

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


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-180n+360/n+120=0

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}
$