0=16t^2+44t+8

Solution for 0=16t^2+44t+8 equation:

0=16t^2+44t+8

We move all terms to the left:

0-(16t^2+44t+8)=0

We add all the numbers together, and all the variables

-(16t^2+44t+8)=0

We get rid of parentheses

-16t^2-44t-8=0

a = -16; b = -44; c = -8;
Δ = b2-4ac
Δ = -442-4·(-16)·(-8)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{89}}{2*-16}=\frac{44-4\sqrt{89}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{89}}{2*-16}=\frac{44+4\sqrt{89}}{-32}
$