X^2+y^2=90000

Solution for X^2+y^2=90000 equation:

X^2+X^2=90000

We move all terms to the left:

X^2+X^2-(90000)=0

We add all the numbers together, and all the variables

2X^2-90000=0

a = 2; b = 0; c = -90000;
Δ = b2-4ac
Δ = 02-4·2·(-90000)
Δ = 720000
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:

$\sqrt{\Delta}=\sqrt{720000}=\sqrt{360000*2}=\sqrt{360000}*\sqrt{2}=600\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{2}}{2*2}=\frac{0-600\sqrt{2}}{4}
=-\frac{600\sqrt{2}}{4}
=-150\sqrt{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{2}}{2*2}=\frac{0+600\sqrt{2}}{4}
=\frac{600\sqrt{2}}{4}
=150\sqrt{2}
$