56^2+42^2=c^2

Solution for 56^2+42^2=c^2 equation:

56^2+42^2=c^2

We move all terms to the left:

56^2+42^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+4900=0

a = -1; b = 0; c = +4900;
Δ = b2-4ac
Δ = 02-4·(-1)·4900
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-140}{2*-1}=\frac{-140}{-2}
=+70
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+140}{2*-1}=\frac{140}{-2}
=-70
$