180n-360/n=1800/n

Solution for 180n-360/n=1800/n equation:

180n-360/n=1800/n

We move all terms to the left:

180n-360/n-(1800/n)=0


Domain of the equation: n!=0

n∈R



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-(+1800/n)=0

We get rid of parentheses

180n-360/n-1800/n=0

We multiply all the terms by the denominator


180n*n-360-1800=0

We add all the numbers together, and all the variables

180n*n-2160=0

Wy multiply elements

180n^2-2160=0

a = 180; b = 0; c = -2160;
Δ = b2-4ac
Δ = 02-4·180·(-2160)
Δ = 1555200
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:

$\sqrt{\Delta}=\sqrt{1555200}=\sqrt{518400*3}=\sqrt{518400}*\sqrt{3}=720\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-720\sqrt{3}}{2*180}=\frac{0-720\sqrt{3}}{360}
=-\frac{720\sqrt{3}}{360}
=-2\sqrt{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+720\sqrt{3}}{2*180}=\frac{0+720\sqrt{3}}{360}
=\frac{720\sqrt{3}}{360}
=2\sqrt{3}
$