4.9t^2+28.7t+4.2=0

Solution for 4.9t^2+28.7t+4.2=0 equation:

Simplifying
4.9t2 + 28.7t + 4.2 = 0

Reorder the terms:
4.2 + 28.7t + 4.9t2 = 0

Solving
4.2 + 28.7t + 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'.
0.8571428571 + 5.857142857t + t2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + 5.857142857t + -0.8571428571 + t2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + 5.857142857t + t2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + 5.857142857t + t2 = 0 + -0.8571428571
5.857142857t + t2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
5.857142857t + t2 = -0.8571428571

The t term is 5.857142857t.  Take half its coefficient (2.928571429).
Square it (8.576530615) and add it to both sides.

Add '8.576530615' to each side of the equation.
5.857142857t + 8.576530615 + t2 = -0.8571428571 + 8.576530615

Reorder the terms:
8.576530615 + 5.857142857t + t2 = -0.8571428571 + 8.576530615

Combine like terms: -0.8571428571 + 8.576530615 = 7.7193877579
8.576530615 + 5.857142857t + t2 = 7.7193877579

Factor a perfect square on the left side:
(t + 2.928571429)(t + 2.928571429) = 7.7193877579

Calculate the square root of the right side: 2.77837862

Break this problem into two subproblems by setting 
(t + 2.928571429) equal to 2.77837862 and -2.77837862.

Subproblem 1
t + 2.928571429 = 2.77837862

Simplifying
t + 2.928571429 = 2.77837862

Reorder the terms:
2.928571429 + t = 2.77837862

Solving
2.928571429 + t = 2.77837862

Solving for variable 't'.

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

Add '-2.928571429' to each side of the equation.
2.928571429 + -2.928571429 + t = 2.77837862 + -2.928571429

Combine like terms: 2.928571429 + -2.928571429 = 0.000000000
0.000000000 + t = 2.77837862 + -2.928571429
t = 2.77837862 + -2.928571429

Combine like terms: 2.77837862 + -2.928571429 = -0.150192809
t = -0.150192809

Simplifying
t = -0.150192809

Subproblem 2
t + 2.928571429 = -2.77837862

Simplifying
t + 2.928571429 = -2.77837862

Reorder the terms:
2.928571429 + t = -2.77837862

Solving
2.928571429 + t = -2.77837862

Solving for variable 't'.

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

Add '-2.928571429' to each side of the equation.
2.928571429 + -2.928571429 + t = -2.77837862 + -2.928571429

Combine like terms: 2.928571429 + -2.928571429 = 0.000000000
0.000000000 + t = -2.77837862 + -2.928571429
t = -2.77837862 + -2.928571429

Combine like terms: -2.77837862 + -2.928571429 = -5.706950049
t = -5.706950049

Simplifying
t = -5.706950049

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.150192809, -5.706950049}