30^2+40^2=c^2

Solution for 30^2+40^2=c^2 equation:

30^2+40^2=c^2

We move all terms to the left:

30^2+40^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+2500=0

a = -1; b = 0; c = +2500;
Δ = b2-4ac
Δ = 02-4·(-1)·2500
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*-1}=\frac{-100}{-2}
=+50
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*-1}=\frac{100}{-2}
=-50
$