H(t)=-16t^2+150t+1

Solution for H(t)=-16t^2+150t+1 equation:

(H)=-16H^2+150H+1

We move all terms to the left:

(H)-(-16H^2+150H+1)=0

We get rid of parentheses

16H^2-150H+H-1=0

We add all the numbers together, and all the variables

16H^2-149H-1=0

a = 16; b = -149; c = -1;
Δ = b2-4ac
Δ = -1492-4·16·(-1)
Δ = 22265
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{-(-149)-\sqrt{22265}}{2*16}=\frac{149-\sqrt{22265}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-149)+\sqrt{22265}}{2*16}=\frac{149+\sqrt{22265}}{32}
$