6=6t+4.905t^2

Solution for 6=6t+4.905t^2 equation:

6=6t+4.905t^2

We move all terms to the left:

6-(6t+4.905t^2)=0

We get rid of parentheses

-4.905t^2-6t+6=0

a = -4.905; b = -6; c = +6;
Δ = b2-4ac
Δ = -62-4·(-4.905)·6
Δ = 153.72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-\sqrt{153.72}}{2*-4.905}=\frac{6-\sqrt{153.72}}{-9.81}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{153.72}}{2*-4.905}=\frac{6+\sqrt{153.72}}{-9.81}
$