21=24t-3t^2

Solution for 21=24t-3t^2 equation:

21=24t-3t^2

We move all terms to the left:

21-(24t-3t^2)=0

We get rid of parentheses

3t^2-24t+21=0

a = 3; b = -24; c = +21;
Δ = b2-4ac
Δ = -242-4·3·21
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18}{2*3}=\frac{6}{6}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18}{2*3}=\frac{42}{6}
=7
$