.5=16t^2+8t

Solution for .5=16t^2+8t equation:

.5=16t^2+8t

We move all terms to the left:

.5-(16t^2+8t)=0

We add all the numbers together, and all the variables

-(16t^2+8t)+0.5=0

We get rid of parentheses

-16t^2-8t+0.5=0

a = -16; b = -8; c = +0.5;
Δ = b2-4ac
Δ = -82-4·(-16)·0.5
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*-16}=\frac{8-4\sqrt{6}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*-16}=\frac{8+4\sqrt{6}}{-32}
$