30a^2-4a+54=0

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Solution for 30a^2-4a+54=0 equation: 


Simplifying
30a2 + -4a + 54 = 0

Reorder the terms:
54 + -4a + 30a2 = 0

Solving
54 + -4a + 30a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -2a + 15a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(27 + -2a + 15a2)' equal to zero and attempt to solve:

Simplifying
27 + -2a + 15a2 = 0

Solving
27 + -2a + 15a2 = 0

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

Divide each side by '15'.
1.8 + -0.1333333333a + a2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + -0.1333333333a + -1.8 + a2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + -0.1333333333a + a2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + -0.1333333333a + a2 = 0 + -1.8
-0.1333333333a + a2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
-0.1333333333a + a2 = -1.8

The a term is -0.1333333333a.  Take half its coefficient (-0.06666666665).
Square it (0.004444444442) and add it to both sides.

Add '0.004444444442' to each side of the equation.
-0.1333333333a + 0.004444444442 + a2 = -1.8 + 0.004444444442

Reorder the terms:
0.004444444442 + -0.1333333333a + a2 = -1.8 + 0.004444444442

Combine like terms: -1.8 + 0.004444444442 = -1.795555555558
0.004444444442 + -0.1333333333a + a2 = -1.795555555558

Factor a perfect square on the left side:
(a + -0.06666666665)(a + -0.06666666665) = -1.795555555558

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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