4x^2-3x-12=0

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


Simplifying
4x2 + -3x + -12 = 0

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

Solving
-12 + -3x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-3 + -0.75x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -0.75x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -0.75x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -0.75x + x2 = 0 + 3
-0.75x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-0.75x + x2 = 3

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 3 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 3 + 0.140625

Combine like terms: 3 + 0.140625 = 3.140625
0.140625 + -0.75x + x2 = 3.140625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 3.140625

Calculate the square root of the right side: 1.77218086

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.77218086 and -1.77218086.


Subproblem 1
x + -0.375 = 1.77218086

Simplifying
x + -0.375 = 1.77218086

Reorder the terms:
-0.375 + x = 1.77218086

Solving
-0.375 + x = 1.77218086

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.77218086 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.77218086 + 0.375
x = 1.77218086 + 0.375

Combine like terms: 1.77218086 + 0.375 = 2.14718086
x = 2.14718086

Simplifying
x = 2.14718086


Subproblem 2
x + -0.375 = -1.77218086

Simplifying
x + -0.375 = -1.77218086

Reorder the terms:
-0.375 + x = -1.77218086

Solving
-0.375 + x = -1.77218086

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.77218086 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.77218086 + 0.375
x = -1.77218086 + 0.375

Combine like terms: -1.77218086 + 0.375 = -1.39718086
x = -1.39718086

Simplifying
x = -1.39718086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.14718086, -1.39718086}

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