Y=-16t^2+64t+192

Solution for Y=-16t^2+64t+192 equation:

=-16Y^2+64Y+192

We move all terms to the left:

-(-16Y^2+64Y+192)=0

We get rid of parentheses

16Y^2-64Y-192=0

a = 16; b = -64; c = -192;
Δ = b2-4ac
Δ = -642-4·16·(-192)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-128}{2*16}=\frac{-64}{32}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+128}{2*16}=\frac{192}{32}
=6
$