-16t^2+34.14t+43.89=0

Solution for -16t^2+34.14t+43.89=0 equation:

-16t^2+34.14t+43.89=0

a = -16; b = 34.14; c = +43.89;
Δ = b2-4ac
Δ = 34.142-4·(-16)·43.89
Δ = 3974.4996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34.14)-\sqrt{3974.4996}}{2*-16}=\frac{-34.14-\sqrt{3974.4996}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34.14)+\sqrt{3974.4996}}{2*-16}=\frac{-34.14+\sqrt{3974.4996}}{-32}
$