50=-4.9t^2+39.2t+3

Solution for 50=-4.9t^2+39.2t+3 equation:

50=-4.9t^2+39.2t+3

We move all terms to the left:

50-(-4.9t^2+39.2t+3)=0

We get rid of parentheses

4.9t^2-39.2t-3+50=0

We add all the numbers together, and all the variables

4.9t^2-39.2t+47=0

a = 4.9; b = -39.2; c = +47;
Δ = b2-4ac
Δ = -39.22-4·4.9·47
Δ = 615.44
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{-(-39.2)-\sqrt{615.44}}{2*4.9}=\frac{39.2-\sqrt{615.44}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39.2)+\sqrt{615.44}}{2*4.9}=\frac{39.2+\sqrt{615.44}}{9.8}
$