0=-4.9t^2+38.5t+5.6

Solution for 0=-4.9t^2+38.5t+5.6 equation:

0=-4.9t^2+38.5t+5.6

We move all terms to the left:

0-(-4.9t^2+38.5t+5.6)=0

We add all the numbers together, and all the variables

-(-4.9t^2+38.5t+5.6)=0

We get rid of parentheses

4.9t^2-38.5t-5.6=0

a = 4.9; b = -38.5; c = -5.6;
Δ = b2-4ac
Δ = -38.52-4·4.9·(-5.6)
Δ = 1592.01
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{-(-38.5)-\sqrt{1592.01}}{2*4.9}=\frac{38.5-\sqrt{1592.01}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38.5)+\sqrt{1592.01}}{2*4.9}=\frac{38.5+\sqrt{1592.01}}{9.8}
$