150=180n-360/n

Solution for 150=180n-360/n equation:

150=180n-360/n

We move all terms to the left:

150-(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)+150=0

We get rid of parentheses

-180n+360/n+150=0

We multiply all the terms by the denominator


-180n*n+150*n+360=0

We add all the numbers together, and all the variables

150n-180n*n+360=0

Wy multiply elements

-180n^2+150n+360=0

a = -180; b = 150; c = +360;
Δ = b2-4ac
Δ = 1502-4·(-180)·360
Δ = 281700
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:

$\sqrt{\Delta}=\sqrt{281700}=\sqrt{900*313}=\sqrt{900}*\sqrt{313}=30\sqrt{313}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-30\sqrt{313}}{2*-180}=\frac{-150-30\sqrt{313}}{-360}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+30\sqrt{313}}{2*-180}=\frac{-150+30\sqrt{313}}{-360}
$