4^2+4^2=c^2

Solution for 4^2+4^2=c^2 equation:

4^2+4^2=c^2

We move all terms to the left:

4^2+4^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+32=0

a = -1; b = 0; c = +32;
Δ = b2-4ac
Δ = 02-4·(-1)·32
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*-1}=\frac{0-8\sqrt{2}}{-2}
=-\frac{8\sqrt{2}}{-2}
=-\frac{4\sqrt{2}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*-1}=\frac{0+8\sqrt{2}}{-2}
=\frac{8\sqrt{2}}{-2}
=\frac{4\sqrt{2}}{-1}
$