X^2+y^2=4356

Solution for X^2+y^2=4356 equation:

X^2+X^2=4356

We move all terms to the left:

X^2+X^2-(4356)=0

We add all the numbers together, and all the variables

2X^2-4356=0

a = 2; b = 0; c = -4356;
Δ = b2-4ac
Δ = 02-4·2·(-4356)
Δ = 34848
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:

$\sqrt{\Delta}=\sqrt{34848}=\sqrt{17424*2}=\sqrt{17424}*\sqrt{2}=132\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-132\sqrt{2}}{2*2}=\frac{0-132\sqrt{2}}{4}
=-\frac{132\sqrt{2}}{4}
=-33\sqrt{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+132\sqrt{2}}{2*2}=\frac{0+132\sqrt{2}}{4}
=\frac{132\sqrt{2}}{4}
=33\sqrt{2}
$