12x^2+4x-3=0

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


Simplifying
12x2 + 4x + -3 = 0

Reorder the terms:
-3 + 4x + 12x2 = 0

Solving
-3 + 4x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-0.25 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.3333333333x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.3333333333x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.3333333333x + x2 = 0 + 0.25
0.3333333333x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.3333333333x + x2 = 0.25

The x term is 0.3333333333x.  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.
0.3333333333x + 0.02777777779 + x2 = 0.25 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.25 + 0.02777777779

Combine like terms: 0.25 + 0.02777777779 = 0.27777777779
0.02777777779 + 0.3333333333x + x2 = 0.27777777779

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

Calculate the square root of the right side: 0.527046277

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


Subproblem 1
x + 0.1666666667 = 0.527046277

Simplifying
x + 0.1666666667 = 0.527046277

Reorder the terms:
0.1666666667 + x = 0.527046277

Solving
0.1666666667 + x = 0.527046277

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 0.3603796103


Subproblem 2
x + 0.1666666667 = -0.527046277

Simplifying
x + 0.1666666667 = -0.527046277

Reorder the terms:
0.1666666667 + x = -0.527046277

Solving
0.1666666667 + x = -0.527046277

Solving for variable 'x'.

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

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

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

Combine like terms: -0.527046277 + -0.1666666667 = -0.6937129437
x = -0.6937129437

Simplifying
x = -0.6937129437


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

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