8^2+21^2=h^2

Solution for 8^2+21^2=h^2 equation:

8^2+21^2=h^2

We move all terms to the left:

8^2+21^2-(h^2)=0

We add all the numbers together, and all the variables

-1h^2+505=0

a = -1; b = 0; c = +505;
Δ = b2-4ac
Δ = 02-4·(-1)·505
Δ = 2020
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:

$\sqrt{\Delta}=\sqrt{2020}=\sqrt{4*505}=\sqrt{4}*\sqrt{505}=2\sqrt{505}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{505}}{2*-1}=\frac{0-2\sqrt{505}}{-2}
=-\frac{2\sqrt{505}}{-2}
=-\frac{\sqrt{505}}{-1}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{505}}{2*-1}=\frac{0+2\sqrt{505}}{-2}
=\frac{2\sqrt{505}}{-2}
=\frac{\sqrt{505}}{-1}
$