6=2+18t-16t^2

Solution for 6=2+18t-16t^2 equation:

6=2+18t-16t^2

We move all terms to the left:

6-(2+18t-16t^2)=0

We get rid of parentheses

16t^2-18t-2+6=0

We add all the numbers together, and all the variables

16t^2-18t+4=0

a = 16; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·16·4
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{17}}{2*16}=\frac{18-2\sqrt{17}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{17}}{2*16}=\frac{18+2\sqrt{17}}{32}
$