0=16t^2+96t+6

Solution for 0=16t^2+96t+6 equation:

0=16t^2+96t+6

We move all terms to the left:

0-(16t^2+96t+6)=0

We add all the numbers together, and all the variables

-(16t^2+96t+6)=0

We get rid of parentheses

-16t^2-96t-6=0

a = -16; b = -96; c = -6;
Δ = b2-4ac
Δ = -962-4·(-16)·(-6)
Δ = 8832
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:

$\sqrt{\Delta}=\sqrt{8832}=\sqrt{64*138}=\sqrt{64}*\sqrt{138}=8\sqrt{138}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{138}}{2*-16}=\frac{96-8\sqrt{138}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{138}}{2*-16}=\frac{96+8\sqrt{138}}{-32}
$