16.5^2+16.5^2=c^2

Solution for 16.5^2+16.5^2=c^2 equation:

16.5^2+16.5^2=c^2

We move all terms to the left:

16.5^2+16.5^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+544.5=0

a = -1; b = 0; c = +544.5;
Δ = b2-4ac
Δ = 02-4·(-1)·544.5
Δ = 2178
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:

$\sqrt{\Delta}=\sqrt{2178}=\sqrt{1089*2}=\sqrt{1089}*\sqrt{2}=33\sqrt{2}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-33\sqrt{2}}{2*-1}=\frac{0-33\sqrt{2}}{-2}
=-\frac{33\sqrt{2}}{-2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+33\sqrt{2}}{2*-1}=\frac{0+33\sqrt{2}}{-2}
=\frac{33\sqrt{2}}{-2}
$