55^2+73^2=h^2

Solution for 55^2+73^2=h^2 equation:

55^2+73^2=h^2

We move all terms to the left:

55^2+73^2-(h^2)=0

We add all the numbers together, and all the variables

-1h^2+8354=0

a = -1; b = 0; c = +8354;
Δ = b2-4ac
Δ = 02-4·(-1)·8354
Δ = 33416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{33416}=\sqrt{4*8354}=\sqrt{4}*\sqrt{8354}=2\sqrt{8354}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{8354}}{2*-1}=\frac{0-2\sqrt{8354}}{-2}
=-\frac{2\sqrt{8354}}{-2}
=-\frac{\sqrt{8354}}{-1}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{8354}}{2*-1}=\frac{0+2\sqrt{8354}}{-2}
=\frac{2\sqrt{8354}}{-2}
=\frac{\sqrt{8354}}{-1}
$