0=-4.9t^2+30t+6

Solution for 0=-4.9t^2+30t+6 equation:

0=-4.9t^2+30t+6

We move all terms to the left:

0-(-4.9t^2+30t+6)=0

We add all the numbers together, and all the variables

-(-4.9t^2+30t+6)=0

We get rid of parentheses

4.9t^2-30t-6=0

a = 4.9; b = -30; c = -6;
Δ = b2-4ac
Δ = -302-4·4.9·(-6)
Δ = 1017.6
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{-(-30)-\sqrt{1017.6}}{2*4.9}=\frac{30-\sqrt{1017.6}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{1017.6}}{2*4.9}=\frac{30+\sqrt{1017.6}}{9.8}
$