x^2+x^2=12^2

Solution for x^2+x^2=12^2 equation:

x^2+x^2=12^2

We move all terms to the left:

x^2+x^2-(12^2)=0

We add all the numbers together, and all the variables

2x^2-144=0

a = 2; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·2·(-144)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*2}=\frac{0-24\sqrt{2}}{4}
=-\frac{24\sqrt{2}}{4}
=-6\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*2}=\frac{0+24\sqrt{2}}{4}
=\frac{24\sqrt{2}}{4}
=6\sqrt{2}
$