c^2=8^2+17^2

Solution for c^2=8^2+17^2 equation:

c^2=8^2+17^2

We move all terms to the left:

c^2-(8^2+17^2)=0

We add all the numbers together, and all the variables

c^2-353=0

a = 1; b = 0; c = -353;
Δ = b2-4ac
Δ = 02-4·1·(-353)
Δ = 1412
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:

$\sqrt{\Delta}=\sqrt{1412}=\sqrt{4*353}=\sqrt{4}*\sqrt{353}=2\sqrt{353}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{353}}{2*1}=\frac{0-2\sqrt{353}}{2}
=-\frac{2\sqrt{353}}{2}
=-\sqrt{353}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{353}}{2*1}=\frac{0+2\sqrt{353}}{2}
=\frac{2\sqrt{353}}{2}
=\sqrt{353}
$