-4.9t^2+24.5t+9.9=0

Solution for -4.9t^2+24.5t+9.9=0 equation:

-4.9t^2+24.5t+9.9=0

a = -4.9; b = 24.5; c = +9.9;
Δ = b2-4ac
Δ = 24.52-4·(-4.9)·9.9
Δ = 794.29
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{794.29}}{2*-4.9}=\frac{-24.5-\sqrt{794.29}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24.5)+\sqrt{794.29}}{2*-4.9}=\frac{-24.5+\sqrt{794.29}}{-9.8}
$