175/n=180n-360

Solution for 175/n=180n-360 equation:

175/n=180n-360

We move all terms to the left:

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


Domain of the equation: n!=0

n∈R


We get rid of parentheses

175/n-180n+360=0

We multiply all the terms by the denominator


-180n*n+360*n+175=0

We add all the numbers together, and all the variables

360n-180n*n+175=0

Wy multiply elements

-180n^2+360n+175=0

a = -180; b = 360; c = +175;
Δ = b2-4ac
Δ = 3602-4·(-180)·175
Δ = 255600
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:

$\sqrt{\Delta}=\sqrt{255600}=\sqrt{3600*71}=\sqrt{3600}*\sqrt{71}=60\sqrt{71}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-60\sqrt{71}}{2*-180}=\frac{-360-60\sqrt{71}}{-360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+60\sqrt{71}}{2*-180}=\frac{-360+60\sqrt{71}}{-360}
$