H=102-16x^2

Solution for H=102-16x^2 equation:

=102-16H^2

We move all terms to the left:

-(102-16H^2)=0

We get rid of parentheses

16H^2-102=0

a = 16; b = 0; c = -102;
Δ = b2-4ac
Δ = 02-4·16·(-102)
Δ = 6528
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:

$\sqrt{\Delta}=\sqrt{6528}=\sqrt{64*102}=\sqrt{64}*\sqrt{102}=8\sqrt{102}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{102}}{2*16}=\frac{0-8\sqrt{102}}{32}
=-\frac{8\sqrt{102}}{32}
=-\frac{\sqrt{102}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{102}}{2*16}=\frac{0+8\sqrt{102}}{32}
=\frac{8\sqrt{102}}{32}
=\frac{\sqrt{102}}{4}
$