X^2+y^2=104

Solution for X^2+y^2=104 equation:

X^2+X^2=104

We move all terms to the left:

X^2+X^2-(104)=0

We add all the numbers together, and all the variables

2X^2-104=0

a = 2; b = 0; c = -104;
Δ = b2-4ac
Δ = 02-4·2·(-104)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{13}}{2*2}=\frac{0-8\sqrt{13}}{4}
=-\frac{8\sqrt{13}}{4}
=-2\sqrt{13}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{13}}{2*2}=\frac{0+8\sqrt{13}}{4}
=\frac{8\sqrt{13}}{4}
=2\sqrt{13}
$