X^2+y^2=507

Solution for X^2+y^2=507 equation:

X^2+X^2=507

We move all terms to the left:

X^2+X^2-(507)=0

We add all the numbers together, and all the variables

2X^2-507=0

a = 2; b = 0; c = -507;
Δ = b2-4ac
Δ = 02-4·2·(-507)
Δ = 4056
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:

$\sqrt{\Delta}=\sqrt{4056}=\sqrt{676*6}=\sqrt{676}*\sqrt{6}=26\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{6}}{2*2}=\frac{0-26\sqrt{6}}{4}
=-\frac{26\sqrt{6}}{4}
=-\frac{13\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{6}}{2*2}=\frac{0+26\sqrt{6}}{4}
=\frac{26\sqrt{6}}{4}
=\frac{13\sqrt{6}}{2}
$