H(t)=-16t^2+192t+121

Solution for H(t)=-16t^2+192t+121 equation:

(H)=-16H^2+192H+121

We move all terms to the left:

(H)-(-16H^2+192H+121)=0

We get rid of parentheses

16H^2-192H+H-121=0

We add all the numbers together, and all the variables

16H^2-191H-121=0

a = 16; b = -191; c = -121;
Δ = b2-4ac
Δ = -1912-4·16·(-121)
Δ = 44225
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:

$\sqrt{\Delta}=\sqrt{44225}=\sqrt{25*1769}=\sqrt{25}*\sqrt{1769}=5\sqrt{1769}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-191)-5\sqrt{1769}}{2*16}=\frac{191-5\sqrt{1769}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-191)+5\sqrt{1769}}{2*16}=\frac{191+5\sqrt{1769}}{32}
$