1.5=-16t^2+48t+64

Solution for 1.5=-16t^2+48t+64 equation:

1.5=-16t^2+48t+64

We move all terms to the left:

1.5-(-16t^2+48t+64)=0

We get rid of parentheses

16t^2-48t-64+1.5=0

We add all the numbers together, and all the variables

16t^2-48t-62.5=0

a = 16; b = -48; c = -62.5;
Δ = b2-4ac
Δ = -482-4·16·(-62.5)
Δ = 6304
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:

$\sqrt{\Delta}=\sqrt{6304}=\sqrt{16*394}=\sqrt{16}*\sqrt{394}=4\sqrt{394}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{394}}{2*16}=\frac{48-4\sqrt{394}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{394}}{2*16}=\frac{48+4\sqrt{394}}{32}
$