30x^2-39x+4=0

Solution for 30x^2-39x+4=0 equation:

Simplifying
30x2 + -39x + 4 = 0

Reorder the terms:
4 + -39x + 30x2 = 0

Solving
4 + -39x + 30x2 = 0

Solving for variable 'x'.

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

Divide each side by '30'.
0.1333333333 + -1.3x + x2 = 0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + -1.3x + -0.1333333333 + x2 = 0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + -1.3x + x2 = 0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + -1.3x + x2 = 0 + -0.1333333333
-1.3x + x2 = 0 + -0.1333333333

Combine like terms: 0 + -0.1333333333 = -0.1333333333
-1.3x + x2 = -0.1333333333

The x term is -1.3x.  Take half its coefficient (-0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
-1.3x + 0.4225 + x2 = -0.1333333333 + 0.4225

Reorder the terms:
0.4225 + -1.3x + x2 = -0.1333333333 + 0.4225

Combine like terms: -0.1333333333 + 0.4225 = 0.2891666667
0.4225 + -1.3x + x2 = 0.2891666667

Factor a perfect square on the left side:
(x + -0.65)(x + -0.65) = 0.2891666667

Calculate the square root of the right side: 0.537742194

Break this problem into two subproblems by setting 
(x + -0.65) equal to 0.537742194 and -0.537742194.

Subproblem 1
x + -0.65 = 0.537742194

Simplifying
x + -0.65 = 0.537742194

Reorder the terms:
-0.65 + x = 0.537742194

Solving
-0.65 + x = 0.537742194

Solving for variable 'x'.

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

Add '0.65' to each side of the equation.
-0.65 + 0.65 + x = 0.537742194 + 0.65

Combine like terms: -0.65 + 0.65 = 0.00
0.00 + x = 0.537742194 + 0.65
x = 0.537742194 + 0.65

Combine like terms: 0.537742194 + 0.65 = 1.187742194
x = 1.187742194

Simplifying
x = 1.187742194

Subproblem 2
x + -0.65 = -0.537742194

Simplifying
x + -0.65 = -0.537742194

Reorder the terms:
-0.65 + x = -0.537742194

Solving
-0.65 + x = -0.537742194

Solving for variable 'x'.

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

Add '0.65' to each side of the equation.
-0.65 + 0.65 + x = -0.537742194 + 0.65

Combine like terms: -0.65 + 0.65 = 0.00
0.00 + x = -0.537742194 + 0.65
x = -0.537742194 + 0.65

Combine like terms: -0.537742194 + 0.65 = 0.112257806
x = 0.112257806

Simplifying
x = 0.112257806

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.187742194, 0.112257806}