110^2+60^2=c^2

Solution for 110^2+60^2=c^2 equation:

110^2+60^2=c^2

We move all terms to the left:

110^2+60^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+15700=0

a = -1; b = 0; c = +15700;
Δ = b2-4ac
Δ = 02-4·(-1)·15700
Δ = 62800
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:

$\sqrt{\Delta}=\sqrt{62800}=\sqrt{400*157}=\sqrt{400}*\sqrt{157}=20\sqrt{157}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{157}}{2*-1}=\frac{0-20\sqrt{157}}{-2}
=-\frac{20\sqrt{157}}{-2}
=-\frac{10\sqrt{157}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{157}}{2*-1}=\frac{0+20\sqrt{157}}{-2}
=\frac{20\sqrt{157}}{-2}
=\frac{10\sqrt{157}}{-1}
$