x^2+39^2=65^2

Solution for x^2+39^2=65^2 equation:

x^2+39^2=65^2

We move all terms to the left:

x^2+39^2-(65^2)=0

We add all the numbers together, and all the variables

x^2-2704=0

a = 1; b = 0; c = -2704;
Δ = b2-4ac
Δ = 02-4·1·(-2704)
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-104}{2*1}=\frac{-104}{2}
=-52
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+104}{2*1}=\frac{104}{2}
=52
$