12*12+5*5=c*c

Solution for 12*12+5*5=c*c equation:

12*12+5*5=c*c

We move all terms to the left:

12*12+5*5-(c*c)=0

We add all the numbers together, and all the variables

-(+c*c)+12*12+5*5=0

We add all the numbers together, and all the variables

-(+c*c)+169=0

We get rid of parentheses

-c*c+169=0

Wy multiply elements

-1c^2+169=0

a = -1; b = 0; c = +169;
Δ = b2-4ac
Δ = 02-4·(-1)·169
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26}{2*-1}=\frac{-26}{-2}
=+13
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26}{2*-1}=\frac{26}{-2}
=-13
$