H(t)=-16t2+32t+200

Solution for H(t)=-16t2+32t+200 equation:

(H)=-16H^2+32H+200

We move all terms to the left:

(H)-(-16H^2+32H+200)=0

We get rid of parentheses

16H^2-32H+H-200=0

We add all the numbers together, and all the variables

16H^2-31H-200=0

a = 16; b = -31; c = -200;
Δ = b2-4ac
Δ = -312-4·16·(-200)
Δ = 13761
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:

$\sqrt{\Delta}=\sqrt{13761}=\sqrt{9*1529}=\sqrt{9}*\sqrt{1529}=3\sqrt{1529}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-3\sqrt{1529}}{2*16}=\frac{31-3\sqrt{1529}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+3\sqrt{1529}}{2*16}=\frac{31+3\sqrt{1529}}{32}
$