Y=-16t^2+384t

Solution for Y=-16t^2+384t equation:

=-16Y^2+384Y

We move all terms to the left:

-(-16Y^2+384Y)=0

We get rid of parentheses

16Y^2-384Y=0

a = 16; b = -384; c = 0;
Δ = b2-4ac
Δ = -3842-4·16·0
Δ = 147456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{147456}=384$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-384}{2*16}=\frac{0}{32}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+384}{2*16}=\frac{768}{32}
=24
$