H(t)=-16t^2+100t+2

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

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

We move all terms to the left:

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

We get rid of parentheses

16H^2-100H+H-2=0

We add all the numbers together, and all the variables

16H^2-99H-2=0

a = 16; b = -99; c = -2;
Δ = b2-4ac
Δ = -992-4·16·(-2)
Δ = 9929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-\sqrt{9929}}{2*16}=\frac{99-\sqrt{9929}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{9929}}{2*16}=\frac{99+\sqrt{9929}}{32}
$