X^2+y^2=21800

Solution for X^2+y^2=21800 equation:

X^2+X^2=21800

We move all terms to the left:

X^2+X^2-(21800)=0

We add all the numbers together, and all the variables

2X^2-21800=0

a = 2; b = 0; c = -21800;
Δ = b2-4ac
Δ = 02-4·2·(-21800)
Δ = 174400
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:

$\sqrt{\Delta}=\sqrt{174400}=\sqrt{1600*109}=\sqrt{1600}*\sqrt{109}=40\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{109}}{2*2}=\frac{0-40\sqrt{109}}{4}
=-\frac{40\sqrt{109}}{4}
=-10\sqrt{109}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{109}}{2*2}=\frac{0+40\sqrt{109}}{4}
=\frac{40\sqrt{109}}{4}
=10\sqrt{109}
$