52^2+29^2=x^2

Solution for 52^2+29^2=x^2 equation:

52^2+29^2=x^2

We move all terms to the left:

52^2+29^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+3545=0

a = -1; b = 0; c = +3545;
Δ = b2-4ac
Δ = 02-4·(-1)·3545
Δ = 14180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14180}=\sqrt{4*3545}=\sqrt{4}*\sqrt{3545}=2\sqrt{3545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3545}}{2*-1}=\frac{0-2\sqrt{3545}}{-2}
=-\frac{2\sqrt{3545}}{-2}
=-\frac{\sqrt{3545}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3545}}{2*-1}=\frac{0+2\sqrt{3545}}{-2}
=\frac{2\sqrt{3545}}{-2}
=\frac{\sqrt{3545}}{-1}
$