28x^2-30x+5=0

Solution for 28x^2-30x+5=0 equation:

Simplifying
28x2 + -30x + 5 = 0

Reorder the terms:
5 + -30x + 28x2 = 0

Solving
5 + -30x + 28x2 = 0

Solving for variable 'x'.

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

Divide each side by '28'.
0.1785714286 + -1.071428571x + x2 = 0

Move the constant term to the right:

Add '-0.1785714286' to each side of the equation.
0.1785714286 + -1.071428571x + -0.1785714286 + x2 = 0 + -0.1785714286

Reorder the terms:
0.1785714286 + -0.1785714286 + -1.071428571x + x2 = 0 + -0.1785714286

Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000
0.0000000000 + -1.071428571x + x2 = 0 + -0.1785714286
-1.071428571x + x2 = 0 + -0.1785714286

Combine like terms: 0 + -0.1785714286 = -0.1785714286
-1.071428571x + x2 = -0.1785714286

The x term is -1.071428571x.  Take half its coefficient (-0.5357142855).
Square it (0.2869897957) and add it to both sides.

Add '0.2869897957' to each side of the equation.
-1.071428571x + 0.2869897957 + x2 = -0.1785714286 + 0.2869897957

Reorder the terms:
0.2869897957 + -1.071428571x + x2 = -0.1785714286 + 0.2869897957

Combine like terms: -0.1785714286 + 0.2869897957 = 0.1084183671
0.2869897957 + -1.071428571x + x2 = 0.1084183671

Factor a perfect square on the left side:
(x + -0.5357142855)(x + -0.5357142855) = 0.1084183671

Calculate the square root of the right side: 0.329269445

Break this problem into two subproblems by setting 
(x + -0.5357142855) equal to 0.329269445 and -0.329269445.

Subproblem 1
x + -0.5357142855 = 0.329269445

Simplifying
x + -0.5357142855 = 0.329269445

Reorder the terms:
-0.5357142855 + x = 0.329269445

Solving
-0.5357142855 + x = 0.329269445

Solving for variable 'x'.

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

Add '0.5357142855' to each side of the equation.
-0.5357142855 + 0.5357142855 + x = 0.329269445 + 0.5357142855

Combine like terms: -0.5357142855 + 0.5357142855 = 0.0000000000
0.0000000000 + x = 0.329269445 + 0.5357142855
x = 0.329269445 + 0.5357142855

Combine like terms: 0.329269445 + 0.5357142855 = 0.8649837305
x = 0.8649837305

Simplifying
x = 0.8649837305

Subproblem 2
x + -0.5357142855 = -0.329269445

Simplifying
x + -0.5357142855 = -0.329269445

Reorder the terms:
-0.5357142855 + x = -0.329269445

Solving
-0.5357142855 + x = -0.329269445

Solving for variable 'x'.

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

Add '0.5357142855' to each side of the equation.
-0.5357142855 + 0.5357142855 + x = -0.329269445 + 0.5357142855

Combine like terms: -0.5357142855 + 0.5357142855 = 0.0000000000
0.0000000000 + x = -0.329269445 + 0.5357142855
x = -0.329269445 + 0.5357142855

Combine like terms: -0.329269445 + 0.5357142855 = 0.2064448405
x = 0.2064448405

Simplifying
x = 0.2064448405

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8649837305, 0.2064448405}