6=180n-360/n

Solution for 6=180n-360/n equation:

6=180n-360/n

We move all terms to the left:

6-(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)+6=0

We get rid of parentheses

-180n+360/n+6=0

We multiply all the terms by the denominator


-180n*n+6*n+360=0

We add all the numbers together, and all the variables

6n-180n*n+360=0

Wy multiply elements

-180n^2+6n+360=0

a = -180; b = 6; c = +360;
Δ = b2-4ac
Δ = 62-4·(-180)·360
Δ = 259236
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:

$\sqrt{\Delta}=\sqrt{259236}=\sqrt{36*7201}=\sqrt{36}*\sqrt{7201}=6\sqrt{7201}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{7201}}{2*-180}=\frac{-6-6\sqrt{7201}}{-360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{7201}}{2*-180}=\frac{-6+6\sqrt{7201}}{-360}
$