156=180n-360/n

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

156=180n-360/n

We move all terms to the left:

156-(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)+156=0

We get rid of parentheses

-180n+360/n+156=0

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}
$