4.9t^2-19.9t-34=0

Solution for 4.9t^2-19.9t-34=0 equation:

4.9t^2-19.9t-34=0

a = 4.9; b = -19.9; c = -34;
Δ = b2-4ac
Δ = -19.92-4·4.9·(-34)
Δ = 1062.41
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{-(-19.9)-\sqrt{1062.41}}{2*4.9}=\frac{19.9-\sqrt{1062.41}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19.9)+\sqrt{1062.41}}{2*4.9}=\frac{19.9+\sqrt{1062.41}}{9.8}
$