17^2+7^2=x^2

Solution for 17^2+7^2=x^2 equation:

17^2+7^2=x^2

We move all terms to the left:

17^2+7^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+338=0

a = -1; b = 0; c = +338;
Δ = b2-4ac
Δ = 02-4·(-1)·338
Δ = 1352
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:

$\sqrt{\Delta}=\sqrt{1352}=\sqrt{676*2}=\sqrt{676}*\sqrt{2}=26\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{2}}{2*-1}=\frac{0-26\sqrt{2}}{-2}
=-\frac{26\sqrt{2}}{-2}
=-\frac{13\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{2}}{2*-1}=\frac{0+26\sqrt{2}}{-2}
=\frac{26\sqrt{2}}{-2}
=\frac{13\sqrt{2}}{-1}
$