50^2+50^2=x^2

Solution for 50^2+50^2=x^2 equation:

50^2+50^2=x^2

We move all terms to the left:

50^2+50^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+5000=0

a = -1; b = 0; c = +5000;
Δ = b2-4ac
Δ = 02-4·(-1)·5000
Δ = 20000
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:

$\sqrt{\Delta}=\sqrt{20000}=\sqrt{10000*2}=\sqrt{10000}*\sqrt{2}=100\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{2}}{2*-1}=\frac{0-100\sqrt{2}}{-2}
=-\frac{100\sqrt{2}}{-2}
=-\frac{50\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{2}}{2*-1}=\frac{0+100\sqrt{2}}{-2}
=\frac{100\sqrt{2}}{-2}
=\frac{50\sqrt{2}}{-1}
$