0=6+24t-16t^2

Solution for 0=6+24t-16t^2 equation:

0=6+24t-16t^2

We move all terms to the left:

0-(6+24t-16t^2)=0

We add all the numbers together, and all the variables

-(6+24t-16t^2)=0

We get rid of parentheses

16t^2-24t-6=0

a = 16; b = -24; c = -6;
Δ = b2-4ac
Δ = -242-4·16·(-6)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{15}}{2*16}=\frac{24-8\sqrt{15}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{15}}{2*16}=\frac{24+8\sqrt{15}}{32}
$