30x^2-8x+20=0

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Solution for 30x^2-8x+20=0 equation: 


Simplifying
30x2 + -8x + 20 = 0

Reorder the terms:
20 + -8x + 30x2 = 0

Solving
20 + -8x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -4x + 15x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + -4x + 15x2)' equal to zero and attempt to solve:

Simplifying
10 + -4x + 15x2 = 0

Solving
10 + -4x + 15x2 = 0

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

Divide each side by '15'.
0.6666666667 + -0.2666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -0.2666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -0.2666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -0.2666666667x + x2 = 0 + -0.6666666667
-0.2666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-0.2666666667x + x2 = -0.6666666667

The x term is -0.2666666667x.  Take half its coefficient (-0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
-0.2666666667x + 0.01777777780 + x2 = -0.6666666667 + 0.01777777780

Reorder the terms:
0.01777777780 + -0.2666666667x + x2 = -0.6666666667 + 0.01777777780

Combine like terms: -0.6666666667 + 0.01777777780 = -0.6488888889
0.01777777780 + -0.2666666667x + x2 = -0.6488888889

Factor a perfect square on the left side:
(x + -0.1333333334)(x + -0.1333333334) = -0.6488888889

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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