H(t)=100t-16t^2+100t+150

Solution for H(t)=100t-16t^2+100t+150 equation:

(H)=100H-16H^2+100H+150

We move all terms to the left:

(H)-(100H-16H^2+100H+150)=0

We get rid of parentheses

16H^2-100H-100H+H-150=0

We add all the numbers together, and all the variables

16H^2-199H-150=0

a = 16; b = -199; c = -150;
Δ = b2-4ac
Δ = -1992-4·16·(-150)
Δ = 49201
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{-(-199)-\sqrt{49201}}{2*16}=\frac{199-\sqrt{49201}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+\sqrt{49201}}{2*16}=\frac{199+\sqrt{49201}}{32}
$