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

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

Simplifying
-4.9t2 + 19.6t + -14.7 = 0

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

Solving
-14.7 + 19.6t + -4.9t2 = 0

Solving for variable 't'.

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

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

Move the constant term to the right:

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

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

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

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

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

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

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

Combine like terms: -3 + 4 = 1
4 + -4t + t2 = 1

Factor a perfect square on the left side:
(t + -2)(t + -2) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(t + -2) equal to 1 and -1.

Subproblem 1
t + -2 = 1

Simplifying
t + -2 = 1

Reorder the terms:
-2 + t = 1

Solving
-2 + t = 1

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 1 + 2

Combine like terms: -2 + 2 = 0
0 + t = 1 + 2
t = 1 + 2

Combine like terms: 1 + 2 = 3
t = 3

Simplifying
t = 3

Subproblem 2
t + -2 = -1

Simplifying
t + -2 = -1

Reorder the terms:
-2 + t = -1

Solving
-2 + t = -1

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -1 + 2

Combine like terms: -2 + 2 = 0
0 + t = -1 + 2
t = -1 + 2

Combine like terms: -1 + 2 = 1
t = 1

Simplifying
t = 1

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3, 1}