0=-16t^2+154t-6

Solution for 0=-16t^2+154t-6 equation:

0=-16t^2+154t-6

We move all terms to the left:

0-(-16t^2+154t-6)=0

We add all the numbers together, and all the variables

-(-16t^2+154t-6)=0

We get rid of parentheses

16t^2-154t+6=0

a = 16; b = -154; c = +6;
Δ = b2-4ac
Δ = -1542-4·16·6
Δ = 23332
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:

$\sqrt{\Delta}=\sqrt{23332}=\sqrt{4*5833}=\sqrt{4}*\sqrt{5833}=2\sqrt{5833}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{5833}}{2*16}=\frac{154-2\sqrt{5833}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{5833}}{2*16}=\frac{154+2\sqrt{5833}}{32}
$