x^2+x^2=128^2

Solution for x^2+x^2=128^2 equation:

x^2+x^2=128^2

We move all terms to the left:

x^2+x^2-(128^2)=0

We add all the numbers together, and all the variables

2x^2-16384=0

a = 2; b = 0; c = -16384;
Δ = b2-4ac
Δ = 02-4·2·(-16384)
Δ = 131072
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:

$\sqrt{\Delta}=\sqrt{131072}=\sqrt{65536*2}=\sqrt{65536}*\sqrt{2}=256\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-256\sqrt{2}}{2*2}=\frac{0-256\sqrt{2}}{4}
=-\frac{256\sqrt{2}}{4}
=-64\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+256\sqrt{2}}{2*2}=\frac{0+256\sqrt{2}}{4}
=\frac{256\sqrt{2}}{4}
=64\sqrt{2}
$