8^2+12^2=c^2

Solution for 8^2+12^2=c^2 equation:

8^2+12^2=c^2

We move all terms to the left:

8^2+12^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+208=0

a = -1; b = 0; c = +208;
Δ = b2-4ac
Δ = 02-4·(-1)·208
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{13}}{2*-1}=\frac{0-8\sqrt{13}}{-2}
=-\frac{8\sqrt{13}}{-2}
=-\frac{4\sqrt{13}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{13}}{2*-1}=\frac{0+8\sqrt{13}}{-2}
=\frac{8\sqrt{13}}{-2}
=\frac{4\sqrt{13}}{-1}
$