502.34^2-321.84^2=b^2

Solution for 502.34^2-321.84^2=b^2 equation:

502.34^2-321.84^2=b^2

We move all terms to the left:

502.34^2-321.84^2-(b^2)=0

We add all the numbers together, and all the variables

-1b^2+148764.49=0

a = -1; b = 0; c = +148764.49;
Δ = b2-4ac
Δ = 02-4·(-1)·148764.49
Δ = 595057.96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{595057.96}}{2*-1}=\frac{0-\sqrt{595057.96}}{-2}
=-\frac{\sqrt{}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{595057.96}}{2*-1}=\frac{0+\sqrt{595057.96}}{-2}
=\frac{\sqrt{}}{-2}
$