12a-4a^2-3=0

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

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

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

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

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.75 + -3a + a2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -3a + -0.75 + a2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -3a + a2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -3a + a2 = 0 + -0.75
-3a + a2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-3a + a2 = -0.75

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -0.75 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -0.75 + 2.25

Combine like terms: -0.75 + 2.25 = 1.5
2.25 + -3a + a2 = 1.5

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(a + -1.5) equal to 1.224744871 and -1.224744871.

Subproblem 1
a + -1.5 = 1.224744871

Simplifying
a + -1.5 = 1.224744871

Reorder the terms:
-1.5 + a = 1.224744871

Solving
-1.5 + a = 1.224744871

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = 1.224744871 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = 1.224744871 + 1.5
a = 1.224744871 + 1.5

Combine like terms: 1.224744871 + 1.5 = 2.724744871
a = 2.724744871

Simplifying
a = 2.724744871

Subproblem 2
a + -1.5 = -1.224744871

Simplifying
a + -1.5 = -1.224744871

Reorder the terms:
-1.5 + a = -1.224744871

Solving
-1.5 + a = -1.224744871

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = -1.224744871 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = -1.224744871 + 1.5
a = -1.224744871 + 1.5

Combine like terms: -1.224744871 + 1.5 = 0.275255129
a = 0.275255129

Simplifying
a = 0.275255129

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.724744871, 0.275255129}