6=-16t^2+40t+5.5

Solution for 6=-16t^2+40t+5.5 equation:

6=-16t^2+40t+5.5

We move all terms to the left:

6-(-16t^2+40t+5.5)=0

We get rid of parentheses

16t^2-40t-5.5+6=0

We add all the numbers together, and all the variables

16t^2-40t+0.5=0

a = 16; b = -40; c = +0.5;
Δ = b2-4ac
Δ = -402-4·16·0.5
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-28\sqrt{2}}{2*16}=\frac{40-28\sqrt{2}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+28\sqrt{2}}{2*16}=\frac{40+28\sqrt{2}}{32}
$