(180)/540=n2

Solution for (180)/540=n2 equation:

(180)/540=n2

We move all terms to the left:

(180)/540-(n2)=0

We add all the numbers together, and all the variables

-1n^2+180/540=0

We multiply all the terms by the denominator


-1n^2*540+180=0

Wy multiply elements

-540n^2+180=0

a = -540; b = 0; c = +180;
Δ = b2-4ac
Δ = 02-4·(-540)·180
Δ = 388800
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:

$\sqrt{\Delta}=\sqrt{388800}=\sqrt{129600*3}=\sqrt{129600}*\sqrt{3}=360\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-360\sqrt{3}}{2*-540}=\frac{0-360\sqrt{3}}{-1080}
=-\frac{360\sqrt{3}}{-1080}
=-\frac{\sqrt{3}}{-3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+360\sqrt{3}}{2*-540}=\frac{0+360\sqrt{3}}{-1080}
=\frac{360\sqrt{3}}{-1080}
=\frac{\sqrt{3}}{-3}
$