5^2+9^2=c^2

Solution for 5^2+9^2=c^2 equation:

5^2+9^2=c^2

We move all terms to the left:

5^2+9^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+106=0

a = -1; b = 0; c = +106;
Δ = b2-4ac
Δ = 02-4·(-1)·106
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{106}}{2*-1}=\frac{0-2\sqrt{106}}{-2}
=-\frac{2\sqrt{106}}{-2}
=-\frac{\sqrt{106}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{106}}{2*-1}=\frac{0+2\sqrt{106}}{-2}
=\frac{2\sqrt{106}}{-2}
=\frac{\sqrt{106}}{-1}
$