0=-3t^2+6t-1

Solution for 0=-3t^2+6t-1 equation:

0=-3t^2+6t-1

We move all terms to the left:

0-(-3t^2+6t-1)=0

We add all the numbers together, and all the variables

-(-3t^2+6t-1)=0

We get rid of parentheses

3t^2-6t+1=0

a = 3; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·3·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{6}}{2*3}=\frac{6-2\sqrt{6}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{6}}{2*3}=\frac{6+2\sqrt{6}}{6}
$