H(2)=100t-16t2

Solution for H(2)=100t-16t2 equation:

(2)=100H-16H^2

We move all terms to the left:

(2)-(100H-16H^2)=0

We get rid of parentheses

16H^2-100H+2=0

a = 16; b = -100; c = +2;
Δ = b2-4ac
Δ = -1002-4·16·2
Δ = 9872
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:

$\sqrt{\Delta}=\sqrt{9872}=\sqrt{16*617}=\sqrt{16}*\sqrt{617}=4\sqrt{617}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{617}}{2*16}=\frac{100-4\sqrt{617}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{617}}{2*16}=\frac{100+4\sqrt{617}}{32}
$