-16t2+38.4t+3.5=0

Solution for -16t2+38.4t+3.5=0 equation:

-16t^2+38.4t+3.5=0

a = -16; b = 38.4; c = +3.5;
Δ = b2-4ac
Δ = 38.42-4·(-16)·3.5
Δ = 1698.56
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{-(38.4)-\sqrt{1698.56}}{2*-16}=\frac{-38.4-\sqrt{1698.56}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38.4)+\sqrt{1698.56}}{2*-16}=\frac{-38.4+\sqrt{1698.56}}{-32}
$