0=-16t^2-8t+24

Solution for 0=-16t^2-8t+24 equation:

0=-16t^2-8t+24

We move all terms to the left:

0-(-16t^2-8t+24)=0

We add all the numbers together, and all the variables

-(-16t^2-8t+24)=0

We get rid of parentheses

16t^2+8t-24=0

a = 16; b = 8; c = -24;
Δ = b2-4ac
Δ = 82-4·16·(-24)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-40}{2*16}=\frac{-48}{32}
=-1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+40}{2*16}=\frac{32}{32}
=1
$