82+212=h2

Solution for 82+212=h2 equation:

82+212=h2

We move all terms to the left:

82+212-(h2)=0

We add all the numbers together, and all the variables

-1h^2+294=0

a = -1; b = 0; c = +294;
Δ = b2-4ac
Δ = 02-4·(-1)·294
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{6}}{2*-1}=\frac{0-14\sqrt{6}}{-2}
=-\frac{14\sqrt{6}}{-2}
=-\frac{7\sqrt{6}}{-1}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{6}}{2*-1}=\frac{0+14\sqrt{6}}{-2}
=\frac{14\sqrt{6}}{-2}
=\frac{7\sqrt{6}}{-1}
$