12a^2-4a-3=0

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Solution for 12a^2-4a-3=0 equation: 


Simplifying
12a2 + -4a + -3 = 0

Reorder the terms:
-3 + -4a + 12a2 = 0

Solving
-3 + -4a + 12a2 = 0

Solving for variable 'a'.

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

Divide each side by '12'.
-0.25 + -0.3333333333a + a2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.3333333333a + 0.25 + a2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.3333333333a + a2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.3333333333a + a2 = 0 + 0.25
-0.3333333333a + a2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.3333333333a + a2 = 0.25

The a term is -0.3333333333a.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333a + 0.02777777779 + a2 = 0.25 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333a + a2 = 0.25 + 0.02777777779

Combine like terms: 0.25 + 0.02777777779 = 0.27777777779
0.02777777779 + -0.3333333333a + a2 = 0.27777777779

Factor a perfect square on the left side:
(a + -0.1666666667)(a + -0.1666666667) = 0.27777777779

Calculate the square root of the right side: 0.527046277

Break this problem into two subproblems by setting 
(a + -0.1666666667) equal to 0.527046277 and -0.527046277.


Subproblem 1
a + -0.1666666667 = 0.527046277

Simplifying
a + -0.1666666667 = 0.527046277

Reorder the terms:
-0.1666666667 + a = 0.527046277

Solving
-0.1666666667 + a = 0.527046277

Solving for variable 'a'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + a = 0.527046277 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + a = 0.527046277 + 0.1666666667
a = 0.527046277 + 0.1666666667

Combine like terms: 0.527046277 + 0.1666666667 = 0.6937129437
a = 0.6937129437

Simplifying
a = 0.6937129437


Subproblem 2
a + -0.1666666667 = -0.527046277

Simplifying
a + -0.1666666667 = -0.527046277

Reorder the terms:
-0.1666666667 + a = -0.527046277

Solving
-0.1666666667 + a = -0.527046277

Solving for variable 'a'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + a = -0.527046277 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + a = -0.527046277 + 0.1666666667
a = -0.527046277 + 0.1666666667

Combine like terms: -0.527046277 + 0.1666666667 = -0.3603796103
a = -0.3603796103

Simplifying
a = -0.3603796103


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.6937129437, -0.3603796103}

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