12x^2+3x-4=0

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


Simplifying
12x2 + 3x + -4 = 0

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

Solving
-4 + 3x + 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'.
-0.3333333333 + 0.25x + x2 = 0

Move the constant term to the right:

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

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

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.25x + x2 = 0 + 0.3333333333
0.25x + x2 = 0 + 0.3333333333

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

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 0.3333333333 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.3333333333 + 0.015625

Combine like terms: 0.3333333333 + 0.015625 = 0.3489583333
0.015625 + 0.25x + x2 = 0.3489583333

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.3489583333

Calculate the square root of the right side: 0.590726953

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.590726953 and -0.590726953.


Subproblem 1
x + 0.125 = 0.590726953

Simplifying
x + 0.125 = 0.590726953

Reorder the terms:
0.125 + x = 0.590726953

Solving
0.125 + x = 0.590726953

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 0.590726953 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.590726953 + -0.125
x = 0.590726953 + -0.125

Combine like terms: 0.590726953 + -0.125 = 0.465726953
x = 0.465726953

Simplifying
x = 0.465726953


Subproblem 2
x + 0.125 = -0.590726953

Simplifying
x + 0.125 = -0.590726953

Reorder the terms:
0.125 + x = -0.590726953

Solving
0.125 + x = -0.590726953

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -0.590726953 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.590726953 + -0.125
x = -0.590726953 + -0.125

Combine like terms: -0.590726953 + -0.125 = -0.715726953
x = -0.715726953

Simplifying
x = -0.715726953


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.465726953, -0.715726953}

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