x^2+x^2=107^2

Solution for x^2+x^2=107^2 equation:

x^2+x^2=107^2

We move all terms to the left:

x^2+x^2-(107^2)=0

We add all the numbers together, and all the variables

2x^2-11449=0

a = 2; b = 0; c = -11449;
Δ = b2-4ac
Δ = 02-4·2·(-11449)
Δ = 91592
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:

$\sqrt{\Delta}=\sqrt{91592}=\sqrt{45796*2}=\sqrt{45796}*\sqrt{2}=214\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-214\sqrt{2}}{2*2}=\frac{0-214\sqrt{2}}{4}
=-\frac{214\sqrt{2}}{4}
=-\frac{107\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+214\sqrt{2}}{2*2}=\frac{0+214\sqrt{2}}{4}
=\frac{214\sqrt{2}}{4}
=\frac{107\sqrt{2}}{2}
$