S(t)=19.6*t-4.9*t^2

Solution for S(t)=19.6*t-4.9*t^2 equation:

Simplifying
S(t) = 19.6t + -4.9t2

Multiply S * t
tS = 19.6t + -4.9t2

Solving
tS = 19.6t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-19.6t + tS + 4.9t2 = 19.6t + -4.9t2 + -19.6t + 4.9t2

Reorder the terms:
-19.6t + tS + 4.9t2 = 19.6t + -19.6t + -4.9t2 + 4.9t2

Combine like terms: 19.6t + -19.6t = 0.0
-19.6t + tS + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
-19.6t + tS + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-19.6t + tS + 4.9t2 = 0.0

Factor out the Greatest Common Factor (GCF), 't'.
t(-19.6 + S + 4.9t) = 0.0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

Move all terms containing t to the left, all other terms to the right.

Simplifying
t = 0
Subproblem 2
Set the factor '(-19.6 + S + 4.9t)' equal to zero and attempt to solve:

Simplifying
-19.6 + S + 4.9t = 0

Solving
-19.6 + S + 4.9t = 0

Move all terms containing t to the left, all other terms to the right.

Add '19.6' to each side of the equation.
-19.6 + S + 19.6 + 4.9t = 0 + 19.6

Reorder the terms:
-19.6 + 19.6 + S + 4.9t = 0 + 19.6

Combine like terms: -19.6 + 19.6 = 0.0
0.0 + S + 4.9t = 0 + 19.6
S + 4.9t = 0 + 19.6

Combine like terms: 0 + 19.6 = 19.6
S + 4.9t = 19.6

Add '-1S' to each side of the equation.
S + -1S + 4.9t = 19.6 + -1S

Combine like terms: S + -1S = 0
0 + 4.9t = 19.6 + -1S
4.9t = 19.6 + -1S

Divide each side by '4.9'.
t = 4 + -0.2040816327S

Simplifying
t = 4 + -0.2040816327S
Solution
t = {0, 4 + -0.2040816327S}