9=16t2+24t

Solution for 9=16t2+24t equation:

9=16t^2+24t

We move all terms to the left:

9-(16t^2+24t)=0

We get rid of parentheses

-16t^2-24t+9=0

a = -16; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·(-16)·9
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{2}}{2*-16}=\frac{24-24\sqrt{2}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{2}}{2*-16}=\frac{24+24\sqrt{2}}{-32}
$