50^2+100^2=c^2

Solution for 50^2+100^2=c^2 equation:

50^2+100^2=c^2

We move all terms to the left:

50^2+100^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+12500=0

a = -1; b = 0; c = +12500;
Δ = b2-4ac
Δ = 02-4·(-1)·12500
Δ = 50000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{50000}=\sqrt{10000*5}=\sqrt{10000}*\sqrt{5}=100\sqrt{5}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{5}}{2*-1}=\frac{0-100\sqrt{5}}{-2}
=-\frac{100\sqrt{5}}{-2}
=-\frac{50\sqrt{5}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{5}}{2*-1}=\frac{0+100\sqrt{5}}{-2}
=\frac{100\sqrt{5}}{-2}
=\frac{50\sqrt{5}}{-1}
$