21=-16t^2+8t+24

Solution for 21=-16t^2+8t+24 equation:

21=-16t^2+8t+24

We move all terms to the left:

21-(-16t^2+8t+24)=0

We get rid of parentheses

16t^2-8t-24+21=0

We add all the numbers together, and all the variables

16t^2-8t-3=0

a = 16; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·16·(-3)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*16}=\frac{-8}{32}
=-1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*16}=\frac{24}{32}
=3/4
$