Y=-16t^2+24t+48

Solution for Y=-16t^2+24t+48 equation:

=-16Y^2+24Y+48

We move all terms to the left:

-(-16Y^2+24Y+48)=0

We get rid of parentheses

16Y^2-24Y-48=0

a = 16; b = -24; c = -48;
Δ = b2-4ac
Δ = -242-4·16·(-48)
Δ = 3648
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{57}}{2*16}=\frac{24-8\sqrt{57}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{57}}{2*16}=\frac{24+8\sqrt{57}}{32}
$