X=360/n

Solution for X=360/n equation:

X=360/X

We move all terms to the left:

X-(360/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+360/X)=0

We get rid of parentheses

X-360/X=0

We multiply all the terms by the denominator


X*X-360=0

Wy multiply elements

X^2-360=0

a = 1; b = 0; c = -360;
Δ = b2-4ac
Δ = 02-4·1·(-360)
Δ = 1440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*1}=\frac{0-12\sqrt{10}}{2}
=-\frac{12\sqrt{10}}{2}
=-6\sqrt{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*1}=\frac{0+12\sqrt{10}}{2}
=\frac{12\sqrt{10}}{2}
=6\sqrt{10}
$