10^2+x^2=13^2

Solution for 10^2+x^2=13^2 equation:

10^2+x^2=13^2

We move all terms to the left:

10^2+x^2-(13^2)=0

We add all the numbers together, and all the variables

x^2-69=0

a = 1; b = 0; c = -69;
Δ = b2-4ac
Δ = 02-4·1·(-69)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{69}}{2*1}=\frac{0-2\sqrt{69}}{2}
=-\frac{2\sqrt{69}}{2}
=-\sqrt{69}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{69}}{2*1}=\frac{0+2\sqrt{69}}{2}
=\frac{2\sqrt{69}}{2}
=\sqrt{69}
$