24=-16t^2+40t+24

Solution for 24=-16t^2+40t+24 equation:

24=-16t^2+40t+24

We move all terms to the left:

24-(-16t^2+40t+24)=0

We get rid of parentheses

16t^2-40t-24+24=0

We add all the numbers together, and all the variables

16t^2-40t=0

a = 16; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·16·0
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{-(-40)-40}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*16}=\frac{80}{32}
=2+1/2
$