60^2+130^2=c^2

Solution for 60^2+130^2=c^2 equation:

60^2+130^2=c^2

We move all terms to the left:

60^2+130^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+20500=0

a = -1; b = 0; c = +20500;
Δ = b2-4ac
Δ = 02-4·(-1)·20500
Δ = 82000
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:

$\sqrt{\Delta}=\sqrt{82000}=\sqrt{400*205}=\sqrt{400}*\sqrt{205}=20\sqrt{205}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{205}}{2*-1}=\frac{0-20\sqrt{205}}{-2}
=-\frac{20\sqrt{205}}{-2}
=-\frac{10\sqrt{205}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{205}}{2*-1}=\frac{0+20\sqrt{205}}{-2}
=\frac{20\sqrt{205}}{-2}
=\frac{10\sqrt{205}}{-1}
$