17^2+9^2=q^2

Solution for 17^2+9^2=q^2 equation:

17^2+9^2=q^2

We move all terms to the left:

17^2+9^2-(q^2)=0

We add all the numbers together, and all the variables

-1q^2+370=0

a = -1; b = 0; c = +370;
Δ = b2-4ac
Δ = 02-4·(-1)·370
Δ = 1480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1480}=\sqrt{4*370}=\sqrt{4}*\sqrt{370}=2\sqrt{370}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{370}}{2*-1}=\frac{0-2\sqrt{370}}{-2}
=-\frac{2\sqrt{370}}{-2}
=-\frac{\sqrt{370}}{-1}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{370}}{2*-1}=\frac{0+2\sqrt{370}}{-2}
=\frac{2\sqrt{370}}{-2}
=\frac{\sqrt{370}}{-1}
$