-4.9x^2+28.7x+4.2=0

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

Simplifying
-4.9x2 + 28.7x + 4.2 = 0

Reorder the terms:
4.2 + 28.7x + -4.9x2 = 0

Solving
4.2 + 28.7x + -4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '-4.9'.
-0.8571428571 + -5.857142857x + x2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -5.857142857x + 0.8571428571 + x2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -5.857142857x + x2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -5.857142857x + x2 = 0 + 0.8571428571
-5.857142857x + x2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-5.857142857x + x2 = 0.8571428571

The x term is -5.857142857x.  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.
-5.857142857x + 8.576530615 + x2 = 0.8571428571 + 8.576530615

Reorder the terms:
8.576530615 + -5.857142857x + x2 = 0.8571428571 + 8.576530615

Combine like terms: 0.8571428571 + 8.576530615 = 9.4336734721
8.576530615 + -5.857142857x + x2 = 9.4336734721

Factor a perfect square on the left side:
(x + -2.928571429)(x + -2.928571429) = 9.4336734721

Calculate the square root of the right side: 3.071428572

Break this problem into two subproblems by setting 
(x + -2.928571429) equal to 3.071428572 and -3.071428572.

Subproblem 1
x + -2.928571429 = 3.071428572

Simplifying
x + -2.928571429 = 3.071428572

Reorder the terms:
-2.928571429 + x = 3.071428572

Solving
-2.928571429 + x = 3.071428572

Solving for variable 'x'.

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

Add '2.928571429' to each side of the equation.
-2.928571429 + 2.928571429 + x = 3.071428572 + 2.928571429

Combine like terms: -2.928571429 + 2.928571429 = 0.000000000
0.000000000 + x = 3.071428572 + 2.928571429
x = 3.071428572 + 2.928571429

Combine like terms: 3.071428572 + 2.928571429 = 6.000000001
x = 6.000000001

Simplifying
x = 6.000000001

Subproblem 2
x + -2.928571429 = -3.071428572

Simplifying
x + -2.928571429 = -3.071428572

Reorder the terms:
-2.928571429 + x = -3.071428572

Solving
-2.928571429 + x = -3.071428572

Solving for variable 'x'.

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

Add '2.928571429' to each side of the equation.
-2.928571429 + 2.928571429 + x = -3.071428572 + 2.928571429

Combine like terms: -2.928571429 + 2.928571429 = 0.000000000
0.000000000 + x = -3.071428572 + 2.928571429
x = -3.071428572 + 2.928571429

Combine like terms: -3.071428572 + 2.928571429 = -0.142857143
x = -0.142857143

Simplifying
x = -0.142857143

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.000000001, -0.142857143}