20*20+8*8=c*c

Solution for 20*20+8*8=c*c equation:

20*20+8*8=c*c

We move all terms to the left:

20*20+8*8-(c*c)=0

We add all the numbers together, and all the variables

-(+c*c)+20*20+8*8=0

We add all the numbers together, and all the variables

-(+c*c)+464=0

We get rid of parentheses

-c*c+464=0

Wy multiply elements

-1c^2+464=0

a = -1; b = 0; c = +464;
Δ = b2-4ac
Δ = 02-4·(-1)·464
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{29}}{2*-1}=\frac{0-8\sqrt{29}}{-2}
=-\frac{8\sqrt{29}}{-2}
=-\frac{4\sqrt{29}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{29}}{2*-1}=\frac{0+8\sqrt{29}}{-2}
=\frac{8\sqrt{29}}{-2}
=\frac{4\sqrt{29}}{-1}
$