A=180n-360/n

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

=180A-360/A

We move all terms to the left:

-(180A-360/A)=0


Domain of the equation: A)!=0

A!=0/1

A!=0

A∈R


We add all the numbers together, and all the variables

-(+180A-360/A)=0

We get rid of parentheses

-180A+360/A=0

We multiply all the terms by the denominator


-180A*A+360=0

Wy multiply elements

-180A^2+360=0

a = -180; b = 0; c = +360;
Δ = b2-4ac
Δ = 02-4·(-180)·360
Δ = 259200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{259200}=\sqrt{129600*2}=\sqrt{129600}*\sqrt{2}=360\sqrt{2}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-360\sqrt{2}}{2*-180}=\frac{0-360\sqrt{2}}{-360}
=-\frac{360\sqrt{2}}{-360}
=-\frac{\sqrt{2}}{-1}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+360\sqrt{2}}{2*-180}=\frac{0+360\sqrt{2}}{-360}
=\frac{360\sqrt{2}}{-360}
=\frac{\sqrt{2}}{-1}
$