H(t)=-16t^2+55t+60

Solution for H(t)=-16t^2+55t+60 equation:

(H)=-16H^2+55H+60

We move all terms to the left:

(H)-(-16H^2+55H+60)=0

We get rid of parentheses

16H^2-55H+H-60=0

We add all the numbers together, and all the variables

16H^2-54H-60=0

a = 16; b = -54; c = -60;
Δ = b2-4ac
Δ = -542-4·16·(-60)
Δ = 6756
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:

$\sqrt{\Delta}=\sqrt{6756}=\sqrt{4*1689}=\sqrt{4}*\sqrt{1689}=2\sqrt{1689}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{1689}}{2*16}=\frac{54-2\sqrt{1689}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{1689}}{2*16}=\frac{54+2\sqrt{1689}}{32}
$