384=16t^2+27t

Solution for 384=16t^2+27t equation:

384=16t^2+27t

We move all terms to the left:

384-(16t^2+27t)=0

We get rid of parentheses

-16t^2-27t+384=0

a = -16; b = -27; c = +384;
Δ = b2-4ac
Δ = -272-4·(-16)·384
Δ = 25305
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{-(-27)-\sqrt{25305}}{2*-16}=\frac{27-\sqrt{25305}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{25305}}{2*-16}=\frac{27+\sqrt{25305}}{-32}
$