8^2+16^2=b^2

Solution for 8^2+16^2=b^2 equation:

8^2+16^2=b^2

We move all terms to the left:

8^2+16^2-(b^2)=0

We add all the numbers together, and all the variables

-1b^2+320=0

a = -1; b = 0; c = +320;
Δ = b2-4ac
Δ = 02-4·(-1)·320
Δ = 1280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{5}}{2*-1}=\frac{0-16\sqrt{5}}{-2}
=-\frac{16\sqrt{5}}{-2}
=-\frac{8\sqrt{5}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{5}}{2*-1}=\frac{0+16\sqrt{5}}{-2}
=\frac{16\sqrt{5}}{-2}
=\frac{8\sqrt{5}}{-1}
$