180n-36/n=60

Solution for 180n-36/n=60 equation:

180n-36/n=60

We move all terms to the left:

180n-36/n-(60)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


180n*n-60*n-36=0

We add all the numbers together, and all the variables

-60n+180n*n-36=0

Wy multiply elements

180n^2-60n-36=0

a = 180; b = -60; c = -36;
Δ = b2-4ac
Δ = -602-4·180·(-36)
Δ = 29520
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:

$\sqrt{\Delta}=\sqrt{29520}=\sqrt{144*205}=\sqrt{144}*\sqrt{205}=12\sqrt{205}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{205}}{2*180}=\frac{60-12\sqrt{205}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{205}}{2*180}=\frac{60+12\sqrt{205}}{360}
$