0=-6t^2+24t+6

Solution for 0=-6t^2+24t+6 equation:

0=-6t^2+24t+6

We move all terms to the left:

0-(-6t^2+24t+6)=0

We add all the numbers together, and all the variables

-(-6t^2+24t+6)=0

We get rid of parentheses

6t^2-24t-6=0

a = 6; b = -24; c = -6;
Δ = b2-4ac
Δ = -242-4·6·(-6)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{5}}{2*6}=\frac{24-12\sqrt{5}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{5}}{2*6}=\frac{24+12\sqrt{5}}{12}
$