H(t)=-16t^2+1000t+10

Solution for H(t)=-16t^2+1000t+10 equation:

(H)=-16H^2+1000H+10

We move all terms to the left:

(H)-(-16H^2+1000H+10)=0

We get rid of parentheses

16H^2-1000H+H-10=0

We add all the numbers together, and all the variables

16H^2-999H-10=0

a = 16; b = -999; c = -10;
Δ = b2-4ac
Δ = -9992-4·16·(-10)
Δ = 998641
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{-(-999)-\sqrt{998641}}{2*16}=\frac{999-\sqrt{998641}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-999)+\sqrt{998641}}{2*16}=\frac{999+\sqrt{998641}}{32}
$