X^2+y^2=8180

Solution for X^2+y^2=8180 equation:

X^2+X^2=8180

We move all terms to the left:

X^2+X^2-(8180)=0

We add all the numbers together, and all the variables

2X^2-8180=0

a = 2; b = 0; c = -8180;
Δ = b2-4ac
Δ = 02-4·2·(-8180)
Δ = 65440
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:

$\sqrt{\Delta}=\sqrt{65440}=\sqrt{16*4090}=\sqrt{16}*\sqrt{4090}=4\sqrt{4090}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{4090}}{2*2}=\frac{0-4\sqrt{4090}}{4}
=-\frac{4\sqrt{4090}}{4}
=-\sqrt{4090}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{4090}}{2*2}=\frac{0+4\sqrt{4090}}{4}
=\frac{4\sqrt{4090}}{4}
=\sqrt{4090}
$