40^2+15^2=c^2

Solution for 40^2+15^2=c^2 equation:

40^2+15^2=c^2

We move all terms to the left:

40^2+15^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+1825=0

a = -1; b = 0; c = +1825;
Δ = b2-4ac
Δ = 02-4·(-1)·1825
Δ = 7300
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:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{73}}{2*-1}=\frac{0-10\sqrt{73}}{-2}
=-\frac{10\sqrt{73}}{-2}
=-\frac{5\sqrt{73}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{73}}{2*-1}=\frac{0+10\sqrt{73}}{-2}
=\frac{10\sqrt{73}}{-2}
=\frac{5\sqrt{73}}{-1}
$