(13)2+(17)2=(c)2

Solution for (13)2+(17)2=(c)2 equation:

(13)2+(17)2=(c)2

We move all terms to the left:

(13)2+(17)2-((c)2)=0

determiningTheFunctionDomain
-c2+132+172=0

We add all the numbers together, and all the variables

-1c^2+304=0

a = -1; b = 0; c = +304;
Δ = b2-4ac
Δ = 02-4·(-1)·304
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{19}}{2*-1}=\frac{0-8\sqrt{19}}{-2}
=-\frac{8\sqrt{19}}{-2}
=-\frac{4\sqrt{19}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{19}}{2*-1}=\frac{0+8\sqrt{19}}{-2}
=\frac{8\sqrt{19}}{-2}
=\frac{4\sqrt{19}}{-1}
$