t=-4.9t^2+9.1t+1.4

Solution for t=-4.9t^2+9.1t+1.4 equation:

Simplifying
t = -4.9t2 + 9.1t + 1.4

Reorder the terms:
t = 1.4 + 9.1t + -4.9t2

Solving
t = 1.4 + 9.1t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-1.4 + t + -9.1t + 4.9t2 = 1.4 + 9.1t + -4.9t2 + -1.4 + -9.1t + 4.9t2

Combine like terms: t + -9.1t = -8.1t
-1.4 + -8.1t + 4.9t2 = 1.4 + 9.1t + -4.9t2 + -1.4 + -9.1t + 4.9t2

Reorder the terms:
-1.4 + -8.1t + 4.9t2 = 1.4 + -1.4 + 9.1t + -9.1t + -4.9t2 + 4.9t2

Combine like terms: 1.4 + -1.4 = 0.0
-1.4 + -8.1t + 4.9t2 = 0.0 + 9.1t + -9.1t + -4.9t2 + 4.9t2
-1.4 + -8.1t + 4.9t2 = 9.1t + -9.1t + -4.9t2 + 4.9t2

Combine like terms: 9.1t + -9.1t = 0.0
-1.4 + -8.1t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
-1.4 + -8.1t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-1.4 + -8.1t + 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'.
-0.2857142857 + -1.653061224t + t2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -1.653061224t + 0.2857142857 + t2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -1.653061224t + t2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -1.653061224t + t2 = 0 + 0.2857142857
-1.653061224t + t2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-1.653061224t + t2 = 0.2857142857

The t term is -1.653061224t.  Take half its coefficient (-0.826530612).
Square it (0.6831528526) and add it to both sides.

Add '0.6831528526' to each side of the equation.
-1.653061224t + 0.6831528526 + t2 = 0.2857142857 + 0.6831528526

Reorder the terms:
0.6831528526 + -1.653061224t + t2 = 0.2857142857 + 0.6831528526

Combine like terms: 0.2857142857 + 0.6831528526 = 0.9688671383
0.6831528526 + -1.653061224t + t2 = 0.9688671383

Factor a perfect square on the left side:
(t + -0.826530612)(t + -0.826530612) = 0.9688671383

Calculate the square root of the right side: 0.984310489

Break this problem into two subproblems by setting 
(t + -0.826530612) equal to 0.984310489 and -0.984310489.

Subproblem 1
t + -0.826530612 = 0.984310489

Simplifying
t + -0.826530612 = 0.984310489

Reorder the terms:
-0.826530612 + t = 0.984310489

Solving
-0.826530612 + t = 0.984310489

Solving for variable 't'.

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

Add '0.826530612' to each side of the equation.
-0.826530612 + 0.826530612 + t = 0.984310489 + 0.826530612

Combine like terms: -0.826530612 + 0.826530612 = 0.000000000
0.000000000 + t = 0.984310489 + 0.826530612
t = 0.984310489 + 0.826530612

Combine like terms: 0.984310489 + 0.826530612 = 1.810841101
t = 1.810841101

Simplifying
t = 1.810841101

Subproblem 2
t + -0.826530612 = -0.984310489

Simplifying
t + -0.826530612 = -0.984310489

Reorder the terms:
-0.826530612 + t = -0.984310489

Solving
-0.826530612 + t = -0.984310489

Solving for variable 't'.

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

Add '0.826530612' to each side of the equation.
-0.826530612 + 0.826530612 + t = -0.984310489 + 0.826530612

Combine like terms: -0.826530612 + 0.826530612 = 0.000000000
0.000000000 + t = -0.984310489 + 0.826530612
t = -0.984310489 + 0.826530612

Combine like terms: -0.984310489 + 0.826530612 = -0.157779877
t = -0.157779877

Simplifying
t = -0.157779877

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.810841101, -0.157779877}