0=-4.9t^2+14.7t+19.6

Solution for 0=-4.9t^2+14.7t+19.6 equation:

Simplifying
0 = -4.9t2 + 14.7t + 19.6

Reorder the terms:
0 = 19.6 + 14.7t + -4.9t2

Solving
0 = 19.6 + 14.7t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + -19.6 = -19.6
-19.6 + -14.7t + 4.9t2 = 19.6 + 14.7t + -4.9t2 + -19.6 + -14.7t + 4.9t2

Reorder the terms:
-19.6 + -14.7t + 4.9t2 = 19.6 + -19.6 + 14.7t + -14.7t + -4.9t2 + 4.9t2

Combine like terms: 19.6 + -19.6 = 0.0
-19.6 + -14.7t + 4.9t2 = 0.0 + 14.7t + -14.7t + -4.9t2 + 4.9t2
-19.6 + -14.7t + 4.9t2 = 14.7t + -14.7t + -4.9t2 + 4.9t2

Combine like terms: 14.7t + -14.7t = 0.0
-19.6 + -14.7t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
-19.6 + -14.7t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-19.6 + -14.7t + 4.9t2 = 0.0

Begin completing the square.  Divide all terms by
4.9 the coefficient of the squared term: 

Divide each side by '4.9'.
-4 + -3t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -3t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + -3t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3t + t2 = 0 + 4
-3t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
-3t + t2 = 4

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 4 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 4 + 2.25

Combine like terms: 4 + 2.25 = 6.25
2.25 + -3t + t2 = 6.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(t + -1.5) equal to 2.5 and -2.5.

Subproblem 1
t + -1.5 = 2.5

Simplifying
t + -1.5 = 2.5

Reorder the terms:
-1.5 + t = 2.5

Solving
-1.5 + t = 2.5

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 2.5 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 2.5 + 1.5
t = 2.5 + 1.5

Combine like terms: 2.5 + 1.5 = 4
t = 4

Simplifying
t = 4

Subproblem 2
t + -1.5 = -2.5

Simplifying
t + -1.5 = -2.5

Reorder the terms:
-1.5 + t = -2.5

Solving
-1.5 + t = -2.5

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -2.5 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -2.5 + 1.5
t = -2.5 + 1.5

Combine like terms: -2.5 + 1.5 = -1
t = -1

Simplifying
t = -1

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4, -1}