H=-16t^2+(43.89)t+34.14

Solution for H=-16t^2+(43.89)t+34.14 equation:

=-16H^2+(43.89)H+34.14

We move all terms to the left:

-(-16H^2+(43.89)H+34.14)=0


We calculate terms in parentheses: -(-16H^2+(43.89)H+34.14), so:

-16H^2+(43.89)H+34.14

We multiply parentheses

-16H^2+43.89H+34.14

Back to the equation:

-(-16H^2+43.89H+34.14)


We get rid of parentheses

16H^2-43.89H-34.14=0

a = 16; b = -43.89; c = -34.14;
Δ = b2-4ac
Δ = -43.892-4·16·(-34.14)
Δ = 4111.2921
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{-(-43.89)-\sqrt{4111.2921}}{2*16}=\frac{43.89-\sqrt{4111.2921}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43.89)+\sqrt{4111.2921}}{2*16}=\frac{43.89+\sqrt{4111.2921}}{32}
$