4.905t^2-5.785t+0.65=0

Solution for 4.905t^2-5.785t+0.65=0 equation:

4.905t^2-5.785t+0.65=0

a = 4.905; b = -5.785; c = +0.65;
Δ = b2-4ac
Δ = -5.7852-4·4.905·0.65
Δ = 20.713225
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{-(-5.785)-\sqrt{20.713225}}{2*4.905}=\frac{5.785-\sqrt{20.713225}}{9.81}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.785)+\sqrt{20.713225}}{2*4.905}=\frac{5.785+\sqrt{20.713225}}{9.81}
$