H(t)=5+79t-16t^2

Solution for H(t)=5+79t-16t^2 equation:

(H)=5+79H-16H^2

We move all terms to the left:

(H)-(5+79H-16H^2)=0

We get rid of parentheses

16H^2-79H+H-5=0

We add all the numbers together, and all the variables

16H^2-78H-5=0

a = 16; b = -78; c = -5;
Δ = b2-4ac
Δ = -782-4·16·(-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{-(-78)-2\sqrt{1601}}{2*16}=\frac{78-2\sqrt{1601}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1601}}{2*16}=\frac{78+2\sqrt{1601}}{32}
$