H(t)=(-16t^2)+168t+9

Solution for H(t)=(-16t^2)+168t+9 equation:

(H)=(-16H^2)+168H+9

We move all terms to the left:

(H)-((-16H^2)+168H+9)=0


We calculate terms in parentheses: -((-16H^2)+168H+9), so:

(-16H^2)+168H+9

We get rid of parentheses

-16H^2+168H+9

Back to the equation:

-(-16H^2+168H+9)


We get rid of parentheses

16H^2-168H+H-9=0

We add all the numbers together, and all the variables

16H^2-167H-9=0

a = 16; b = -167; c = -9;
Δ = b2-4ac
Δ = -1672-4·16·(-9)
Δ = 28465
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{-(-167)-\sqrt{28465}}{2*16}=\frac{167-\sqrt{28465}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-167)+\sqrt{28465}}{2*16}=\frac{167+\sqrt{28465}}{32}
$