x^2+x^2=80^2

Solution for x^2+x^2=80^2 equation:

x^2+x^2=80^2

We move all terms to the left:

x^2+x^2-(80^2)=0

We add all the numbers together, and all the variables

2x^2-6400=0

a = 2; b = 0; c = -6400;
Δ = b2-4ac
Δ = 02-4·2·(-6400)
Δ = 51200
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:

$\sqrt{\Delta}=\sqrt{51200}=\sqrt{25600*2}=\sqrt{25600}*\sqrt{2}=160\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{2}}{2*2}=\frac{0-160\sqrt{2}}{4}
=-\frac{160\sqrt{2}}{4}
=-40\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{2}}{2*2}=\frac{0+160\sqrt{2}}{4}
=\frac{160\sqrt{2}}{4}
=40\sqrt{2}
$