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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16t^2-24t-32=0

a = 16; b = -24; c = -32;
Δ = b2-4ac
Δ = -242-4·16·(-32)
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{41}}{2*16}=\frac{24-8\sqrt{41}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{41}}{2*16}=\frac{24+8\sqrt{41}}{32}
$