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)=0

a = -16; b = 0; c = +384;
Δ = b2-4ac
Δ = 02-4·(-16)·384
Δ = 24576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24576}=\sqrt{4096*6}=\sqrt{4096}*\sqrt{6}=64\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{6}}{2*-16}=\frac{0-64\sqrt{6}}{-32}
=-\frac{64\sqrt{6}}{-32}
=-\frac{2\sqrt{6}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{6}}{2*-16}=\frac{0+64\sqrt{6}}{-32}
=\frac{64\sqrt{6}}{-32}
=\frac{2\sqrt{6}}{-1}
$