H(t)=-16t^2+30t+200

Solution for H(t)=-16t^2+30t+200 equation:

(H)=-16H^2+30H+200

We move all terms to the left:

(H)-(-16H^2+30H+200)=0

We get rid of parentheses

16H^2-30H+H-200=0

We add all the numbers together, and all the variables

16H^2-29H-200=0

a = 16; b = -29; c = -200;
Δ = b2-4ac
Δ = -292-4·16·(-200)
Δ = 13641
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{-(-29)-\sqrt{13641}}{2*16}=\frac{29-\sqrt{13641}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{13641}}{2*16}=\frac{29+\sqrt{13641}}{32}
$