H(t)=-16t^2-85t+3

Solution for H(t)=-16t^2-85t+3 equation:

(H)=-16H^2-85H+3

We move all terms to the left:

(H)-(-16H^2-85H+3)=0

We get rid of parentheses

16H^2+85H+H-3=0

We add all the numbers together, and all the variables

16H^2+86H-3=0

a = 16; b = 86; c = -3;
Δ = b2-4ac
Δ = 862-4·16·(-3)
Δ = 7588
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:

$\sqrt{\Delta}=\sqrt{7588}=\sqrt{4*1897}=\sqrt{4}*\sqrt{1897}=2\sqrt{1897}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-2\sqrt{1897}}{2*16}=\frac{-86-2\sqrt{1897}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+2\sqrt{1897}}{2*16}=\frac{-86+2\sqrt{1897}}{32}
$