H(t)=16t^2+65t+5

Solution for H(t)=16t^2+65t+5 equation:

(H)=16H^2+65H+5

We move all terms to the left:

(H)-(16H^2+65H+5)=0

We get rid of parentheses

-16H^2+H-65H-5=0

We add all the numbers together, and all the variables

-16H^2-64H-5=0

a = -16; b = -64; c = -5;
Δ = b2-4ac
Δ = -642-4·(-16)·(-5)
Δ = 3776
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:

$\sqrt{\Delta}=\sqrt{3776}=\sqrt{64*59}=\sqrt{64}*\sqrt{59}=8\sqrt{59}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{59}}{2*-16}=\frac{64-8\sqrt{59}}{-32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{59}}{2*-16}=\frac{64+8\sqrt{59}}{-32}
$