110^2+35^2=c^2

Solution for 110^2+35^2=c^2 equation:

110^2+35^2=c^2

We move all terms to the left:

110^2+35^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+13325=0

a = -1; b = 0; c = +13325;
Δ = b2-4ac
Δ = 02-4·(-1)·13325
Δ = 53300
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:

$\sqrt{\Delta}=\sqrt{53300}=\sqrt{100*533}=\sqrt{100}*\sqrt{533}=10\sqrt{533}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{533}}{2*-1}=\frac{0-10\sqrt{533}}{-2}
=-\frac{10\sqrt{533}}{-2}
=-\frac{5\sqrt{533}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{533}}{2*-1}=\frac{0+10\sqrt{533}}{-2}
=\frac{10\sqrt{533}}{-2}
=\frac{5\sqrt{533}}{-1}
$