4.905t^2-8.228t=0.65

Solution for 4.905t^2-8.228t=0.65 equation:

4.905t^2-8.228t=0.65

We move all terms to the left:

4.905t^2-8.228t-(0.65)=0

We add all the numbers together, and all the variables

4.905t^2-8.228t-0.65=0

a = 4.905; b = -8.228; c = -0.65;
Δ = b2-4ac
Δ = -8.2282-4·4.905·(-0.65)
Δ = 80.452984
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{-(-8.228)-\sqrt{80.452984}}{2*4.905}=\frac{8.228-\sqrt{80.452984}}{9.81}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.228)+\sqrt{80.452984}}{2*4.905}=\frac{8.228+\sqrt{80.452984}}{9.81}
$