13^2=9^2+x^2

Solution for 13^2=9^2+x^2 equation:

13^2=9^2+x^2

We move all terms to the left:

13^2-(9^2+x^2)=0

We add all the numbers together, and all the variables

-(9^2+x^2)+169=0

We get rid of parentheses

-x^2+169-9^2=0

We add all the numbers together, and all the variables

-1x^2+88=0

a = -1; b = 0; c = +88;
Δ = b2-4ac
Δ = 02-4·(-1)·88
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*-1}=\frac{0-4\sqrt{22}}{-2}
=-\frac{4\sqrt{22}}{-2}
=-\frac{2\sqrt{22}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*-1}=\frac{0+4\sqrt{22}}{-2}
=\frac{4\sqrt{22}}{-2}
=\frac{2\sqrt{22}}{-1}
$