384^2+440^2=c^2

Solution for 384^2+440^2=c^2 equation:

384^2+440^2=c^2

We move all terms to the left:

384^2+440^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+341056=0

a = -1; b = 0; c = +341056;
Δ = b2-4ac
Δ = 02-4·(-1)·341056
Δ = 1364224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1364224}=1168$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1168}{2*-1}=\frac{-1168}{-2}
=+584
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1168}{2*-1}=\frac{1168}{-2}
=-584
$