24.5t+2-4.9t^2=-2

Solution for 24.5t+2-4.9t^2=-2 equation:

24.5t+2-4.9t^2=-2

We move all terms to the left:

24.5t+2-4.9t^2-(-2)=0

We add all the numbers together, and all the variables

-4.9t^2+24.5t+4=0

a = -4.9; b = 24.5; c = +4;
Δ = b2-4ac
Δ = 24.52-4·(-4.9)·4
Δ = 678.65
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{-(24.5)-\sqrt{678.65}}{2*-4.9}=\frac{-24.5-\sqrt{678.65}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24.5)+\sqrt{678.65}}{2*-4.9}=\frac{-24.5+\sqrt{678.65}}{-9.8}
$