t=-4.9t^2+28.7t+4.2

Solution for t=-4.9t^2+28.7t+4.2 equation:

Simplifying
t = -4.9t2 + 28.7t + 4.2

Reorder the terms:
t = 4.2 + 28.7t + -4.9t2

Solving
t = 4.2 + 28.7t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-4.2 + t + -28.7t + 4.9t2 = 4.2 + 28.7t + -4.9t2 + -4.2 + -28.7t + 4.9t2

Combine like terms: t + -28.7t = -27.7t
-4.2 + -27.7t + 4.9t2 = 4.2 + 28.7t + -4.9t2 + -4.2 + -28.7t + 4.9t2

Reorder the terms:
-4.2 + -27.7t + 4.9t2 = 4.2 + -4.2 + 28.7t + -28.7t + -4.9t2 + 4.9t2

Combine like terms: 4.2 + -4.2 = 0.0
-4.2 + -27.7t + 4.9t2 = 0.0 + 28.7t + -28.7t + -4.9t2 + 4.9t2
-4.2 + -27.7t + 4.9t2 = 28.7t + -28.7t + -4.9t2 + 4.9t2

Combine like terms: 28.7t + -28.7t = 0.0
-4.2 + -27.7t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
-4.2 + -27.7t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-4.2 + -27.7t + 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'.
-0.8571428571 + -5.653061224t + t2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -5.653061224t + 0.8571428571 + t2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -5.653061224t + t2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -5.653061224t + t2 = 0 + 0.8571428571
-5.653061224t + t2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-5.653061224t + t2 = 0.8571428571

The t term is -5.653061224t.  Take half its coefficient (-2.826530612).
Square it (7.989275301) and add it to both sides.

Add '7.989275301' to each side of the equation.
-5.653061224t + 7.989275301 + t2 = 0.8571428571 + 7.989275301

Reorder the terms:
7.989275301 + -5.653061224t + t2 = 0.8571428571 + 7.989275301

Combine like terms: 0.8571428571 + 7.989275301 = 8.8464181581
7.989275301 + -5.653061224t + t2 = 8.8464181581

Factor a perfect square on the left side:
(t + -2.826530612)(t + -2.826530612) = 8.8464181581

Calculate the square root of the right side: 2.974292884

Break this problem into two subproblems by setting 
(t + -2.826530612) equal to 2.974292884 and -2.974292884.

Subproblem 1
t + -2.826530612 = 2.974292884

Simplifying
t + -2.826530612 = 2.974292884

Reorder the terms:
-2.826530612 + t = 2.974292884

Solving
-2.826530612 + t = 2.974292884

Solving for variable 't'.

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

Add '2.826530612' to each side of the equation.
-2.826530612 + 2.826530612 + t = 2.974292884 + 2.826530612

Combine like terms: -2.826530612 + 2.826530612 = 0.000000000
0.000000000 + t = 2.974292884 + 2.826530612
t = 2.974292884 + 2.826530612

Combine like terms: 2.974292884 + 2.826530612 = 5.800823496
t = 5.800823496

Simplifying
t = 5.800823496

Subproblem 2
t + -2.826530612 = -2.974292884

Simplifying
t + -2.826530612 = -2.974292884

Reorder the terms:
-2.826530612 + t = -2.974292884

Solving
-2.826530612 + t = -2.974292884

Solving for variable 't'.

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

Add '2.826530612' to each side of the equation.
-2.826530612 + 2.826530612 + t = -2.974292884 + 2.826530612

Combine like terms: -2.826530612 + 2.826530612 = 0.000000000
0.000000000 + t = -2.974292884 + 2.826530612
t = -2.974292884 + 2.826530612

Combine like terms: -2.974292884 + 2.826530612 = -0.147762272
t = -0.147762272

Simplifying
t = -0.147762272

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.800823496, -0.147762272}