X^2+y^2=8000

Solution for X^2+y^2=8000 equation:

X^2+X^2=8000

We move all terms to the left:

X^2+X^2-(8000)=0

We add all the numbers together, and all the variables

2X^2-8000=0

a = 2; b = 0; c = -8000;
Δ = b2-4ac
Δ = 02-4·2·(-8000)
Δ = 64000
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:

$\sqrt{\Delta}=\sqrt{64000}=\sqrt{6400*10}=\sqrt{6400}*\sqrt{10}=80\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{10}}{2*2}=\frac{0-80\sqrt{10}}{4}
=-\frac{80\sqrt{10}}{4}
=-20\sqrt{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{10}}{2*2}=\frac{0+80\sqrt{10}}{4}
=\frac{80\sqrt{10}}{4}
=20\sqrt{10}
$