X^2+y^2=192

Solution for X^2+y^2=192 equation:

X^2+X^2=192

We move all terms to the left:

X^2+X^2-(192)=0

We add all the numbers together, and all the variables

2X^2-192=0

a = 2; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·2·(-192)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*2}=\frac{0-16\sqrt{6}}{4}
=-\frac{16\sqrt{6}}{4}
=-4\sqrt{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*2}=\frac{0+16\sqrt{6}}{4}
=\frac{16\sqrt{6}}{4}
=4\sqrt{6}
$