34*34+54*54=c*c

Solution for 34*34+54*54=c*c equation:

34*34+54*54=c*c

We move all terms to the left:

34*34+54*54-(c*c)=0

We add all the numbers together, and all the variables

-(+c*c)+34*34+54*54=0

We add all the numbers together, and all the variables

-(+c*c)+4072=0

We get rid of parentheses

-c*c+4072=0

Wy multiply elements

-1c^2+4072=0

a = -1; b = 0; c = +4072;
Δ = b2-4ac
Δ = 02-4·(-1)·4072
Δ = 16288
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:

$\sqrt{\Delta}=\sqrt{16288}=\sqrt{16*1018}=\sqrt{16}*\sqrt{1018}=4\sqrt{1018}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1018}}{2*-1}=\frac{0-4\sqrt{1018}}{-2}
=-\frac{4\sqrt{1018}}{-2}
=-\frac{2\sqrt{1018}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1018}}{2*-1}=\frac{0+4\sqrt{1018}}{-2}
=\frac{4\sqrt{1018}}{-2}
=\frac{2\sqrt{1018}}{-1}
$