H(t)=-16t^2+78t+45

Solution for H(t)=-16t^2+78t+45 equation:

(H)=-16H^2+78H+45

We move all terms to the left:

(H)-(-16H^2+78H+45)=0

We get rid of parentheses

16H^2-78H+H-45=0

We add all the numbers together, and all the variables

16H^2-77H-45=0

a = 16; b = -77; c = -45;
Δ = b2-4ac
Δ = -772-4·16·(-45)
Δ = 8809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-\sqrt{8809}}{2*16}=\frac{77-\sqrt{8809}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+\sqrt{8809}}{2*16}=\frac{77+\sqrt{8809}}{32}
$