10^2+10^2=x^2

Solution for 10^2+10^2=x^2 equation:

10^2+10^2=x^2

We move all terms to the left:

10^2+10^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+200=0

a = -1; b = 0; c = +200;
Δ = b2-4ac
Δ = 02-4·(-1)·200
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*-1}=\frac{0-20\sqrt{2}}{-2}
=-\frac{20\sqrt{2}}{-2}
=-\frac{10\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*-1}=\frac{0+20\sqrt{2}}{-2}
=\frac{20\sqrt{2}}{-2}
=\frac{10\sqrt{2}}{-1}
$