17^2+17^2=c^2

Solution for 17^2+17^2=c^2 equation:

17^2+17^2=c^2

We move all terms to the left:

17^2+17^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+578=0

a = -1; b = 0; c = +578;
Δ = b2-4ac
Δ = 02-4·(-1)·578
Δ = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{2}}{2*-1}=\frac{0-34\sqrt{2}}{-2}
=-\frac{34\sqrt{2}}{-2}
=-\frac{17\sqrt{2}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{2}}{2*-1}=\frac{0+34\sqrt{2}}{-2}
=\frac{34\sqrt{2}}{-2}
=\frac{17\sqrt{2}}{-1}
$