H(t)=-16t2+81t+5

Solution for H(t)=-16t2+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^2-80H-5=0

a = 16; b = -80; c = -5;
Δ = b2-4ac
Δ = -802-4·16·(-5)
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{105}}{2*16}=\frac{80-8\sqrt{105}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{105}}{2*16}=\frac{80+8\sqrt{105}}{32}
$