288^2+175^2=c^2

Solution for 288^2+175^2=c^2 equation:

288^2+175^2=c^2

We move all terms to the left:

288^2+175^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+113569=0

a = -1; b = 0; c = +113569;
Δ = b2-4ac
Δ = 02-4·(-1)·113569
Δ = 454276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{454276}=674$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-674}{2*-1}=\frac{-674}{-2}
=+337
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+674}{2*-1}=\frac{674}{-2}
=-337
$