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

Solution for 0=-16t^2+38.4t+3.5 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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}
$