-2=24t-4.9t^2

Solution for -2=24t-4.9t^2 equation:

-2=24t-4.9t^2

We move all terms to the left:

-2-(24t-4.9t^2)=0

We get rid of parentheses

4.9t^2-24t-2=0

a = 4.9; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·4.9·(-2)
Δ = 615.2
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{-(-24)-\sqrt{615.2}}{2*4.9}=\frac{24-\sqrt{615.2}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+\sqrt{615.2}}{2*4.9}=\frac{24+\sqrt{615.2}}{9.8}
$