H(t)=-16t^2+100t+12

Solution for H(t)=-16t^2+100t+12 equation:

(H)=-16H^2+100H+12

We move all terms to the left:

(H)-(-16H^2+100H+12)=0

We get rid of parentheses

16H^2-100H+H-12=0

We add all the numbers together, and all the variables

16H^2-99H-12=0

a = 16; b = -99; c = -12;
Δ = b2-4ac
Δ = -992-4·16·(-12)
Δ = 10569
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{10569}}{2*16}=\frac{99-\sqrt{10569}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{10569}}{2*16}=\frac{99+\sqrt{10569}}{32}
$