H=-16t^2+1112t

Solution for H=-16t^2+1112t equation:

=-16H^2+1112H

We move all terms to the left:

-(-16H^2+1112H)=0

We get rid of parentheses

16H^2-1112H=0

a = 16; b = -1112; c = 0;
Δ = b2-4ac
Δ = -11122-4·16·0
Δ = 1236544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1236544}=1112$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1112)-1112}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1112)+1112}{2*16}=\frac{2224}{32}
=69+1/2
$