180n-360/n=144

Solution for 180n-360/n=144 equation:

180n-360/n=144

We move all terms to the left:

180n-360/n-(144)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


180n*n-144*n-360=0

We add all the numbers together, and all the variables

-144n+180n*n-360=0

Wy multiply elements

180n^2-144n-360=0

a = 180; b = -144; c = -360;
Δ = b2-4ac
Δ = -1442-4·180·(-360)
Δ = 279936
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:

$\sqrt{\Delta}=\sqrt{279936}=\sqrt{46656*6}=\sqrt{46656}*\sqrt{6}=216\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-216\sqrt{6}}{2*180}=\frac{144-216\sqrt{6}}{360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+216\sqrt{6}}{2*180}=\frac{144+216\sqrt{6}}{360}
$