H(t)=-16t^2-81t-5

Solution for H(t)=-16t^2-81t-5 equation:

(H)=-16H^2-81H-5

We move all terms to the left:

(H)-(-16H^2-81H-5)=0

We get rid of parentheses

16H^2+81H+H+5=0

We add all the numbers together, and all the variables

16H^2+82H+5=0

a = 16; b = 82; c = +5;
Δ = b2-4ac
Δ = 822-4·16·5
Δ = 6404
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:

$\sqrt{\Delta}=\sqrt{6404}=\sqrt{4*1601}=\sqrt{4}*\sqrt{1601}=2\sqrt{1601}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{1601}}{2*16}=\frac{-82-2\sqrt{1601}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{1601}}{2*16}=\frac{-82+2\sqrt{1601}}{32}
$