0=28x^2-120x+50

Solution for 0=28x^2-120x+50 equation:

Simplifying
0 = 28x2 + -120x + 50

Reorder the terms:
0 = 50 + -120x + 28x2

Solving
0 = 50 + -120x + 28x2

Solving for variable 'x'.

Combine like terms: 0 + -50 = -50
-50 + 120x + -28x2 = 50 + -120x + 28x2 + -50 + 120x + -28x2

Reorder the terms:
-50 + 120x + -28x2 = 50 + -50 + -120x + 120x + 28x2 + -28x2

Combine like terms: 50 + -50 = 0
-50 + 120x + -28x2 = 0 + -120x + 120x + 28x2 + -28x2
-50 + 120x + -28x2 = -120x + 120x + 28x2 + -28x2

Combine like terms: -120x + 120x = 0
-50 + 120x + -28x2 = 0 + 28x2 + -28x2
-50 + 120x + -28x2 = 28x2 + -28x2

Combine like terms: 28x2 + -28x2 = 0
-50 + 120x + -28x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 60x + -14x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-25 + 60x + -14x2)' equal to zero and attempt to solve:

Simplifying
-25 + 60x + -14x2 = 0

Solving
-25 + 60x + -14x2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
1.785714286 + -4.285714286x + x2 = 0

Move the constant term to the right:

Add '-1.785714286' to each side of the equation.
1.785714286 + -4.285714286x + -1.785714286 + x2 = 0 + -1.785714286

Reorder the terms:
1.785714286 + -1.785714286 + -4.285714286x + x2 = 0 + -1.785714286

Combine like terms: 1.785714286 + -1.785714286 = 0.000000000
0.000000000 + -4.285714286x + x2 = 0 + -1.785714286
-4.285714286x + x2 = 0 + -1.785714286

Combine like terms: 0 + -1.785714286 = -1.785714286
-4.285714286x + x2 = -1.785714286

The x term is -4.285714286x.  Take half its coefficient (-2.142857143).
Square it (4.591836735) and add it to both sides.

Add '4.591836735' to each side of the equation.
-4.285714286x + 4.591836735 + x2 = -1.785714286 + 4.591836735

Reorder the terms:
4.591836735 + -4.285714286x + x2 = -1.785714286 + 4.591836735

Combine like terms: -1.785714286 + 4.591836735 = 2.806122449
4.591836735 + -4.285714286x + x2 = 2.806122449

Factor a perfect square on the left side:
(x + -2.142857143)(x + -2.142857143) = 2.806122449

Calculate the square root of the right side: 1.675148486

Break this problem into two subproblems by setting 
(x + -2.142857143) equal to 1.675148486 and -1.675148486.

Subproblem 1
x + -2.142857143 = 1.675148486

Simplifying
x + -2.142857143 = 1.675148486

Reorder the terms:
-2.142857143 + x = 1.675148486

Solving
-2.142857143 + x = 1.675148486

Solving for variable 'x'.

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

Add '2.142857143' to each side of the equation.
-2.142857143 + 2.142857143 + x = 1.675148486 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + x = 1.675148486 + 2.142857143
x = 1.675148486 + 2.142857143

Combine like terms: 1.675148486 + 2.142857143 = 3.818005629
x = 3.818005629

Simplifying
x = 3.818005629

Subproblem 2
x + -2.142857143 = -1.675148486

Simplifying
x + -2.142857143 = -1.675148486

Reorder the terms:
-2.142857143 + x = -1.675148486

Solving
-2.142857143 + x = -1.675148486

Solving for variable 'x'.

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

Add '2.142857143' to each side of the equation.
-2.142857143 + 2.142857143 + x = -1.675148486 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + x = -1.675148486 + 2.142857143
x = -1.675148486 + 2.142857143

Combine like terms: -1.675148486 + 2.142857143 = 0.467708657
x = 0.467708657

Simplifying
x = 0.467708657

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.818005629, 0.467708657}
Solution
x = {3.818005629, 0.467708657}