H(t)=-16t^2+245t+200

Solution for H(t)=-16t^2+245t+200 equation:

(H)=-16H^2+245H+200

We move all terms to the left:

(H)-(-16H^2+245H+200)=0

We get rid of parentheses

16H^2-245H+H-200=0

We add all the numbers together, and all the variables

16H^2-244H-200=0

a = 16; b = -244; c = -200;
Δ = b2-4ac
Δ = -2442-4·16·(-200)
Δ = 72336
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:

$\sqrt{\Delta}=\sqrt{72336}=\sqrt{16*4521}=\sqrt{16}*\sqrt{4521}=4\sqrt{4521}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-244)-4\sqrt{4521}}{2*16}=\frac{244-4\sqrt{4521}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-244)+4\sqrt{4521}}{2*16}=\frac{244+4\sqrt{4521}}{32}
$