4x^2-6x-156=0

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Solution for 4x^2-6x-156=0 equation: 


Simplifying
4x2 + -6x + -156 = 0

Reorder the terms:
-156 + -6x + 4x2 = 0

Solving
-156 + -6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + -3x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-78 + -3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-78 + -3x + 2x2 = 0

Solving
-78 + -3x + 2x2 = 0

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

Divide each side by '2'.
-39 + -1.5x + x2 = 0

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -1.5x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + -1.5x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -1.5x + x2 = 0 + 39
-1.5x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
-1.5x + x2 = 39

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 39 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 39 + 0.5625

Combine like terms: 39 + 0.5625 = 39.5625
0.5625 + -1.5x + x2 = 39.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 39.5625

Calculate the square root of the right side: 6.289872813

Break this problem into two subproblems by setting 
(x + -0.75) equal to 6.289872813 and -6.289872813.


Subproblem 1
x + -0.75 = 6.289872813

Simplifying
x + -0.75 = 6.289872813

Reorder the terms:
-0.75 + x = 6.289872813

Solving
-0.75 + x = 6.289872813

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 6.289872813 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 6.289872813 + 0.75
x = 6.289872813 + 0.75

Combine like terms: 6.289872813 + 0.75 = 7.039872813
x = 7.039872813

Simplifying
x = 7.039872813


Subproblem 2
x + -0.75 = -6.289872813

Simplifying
x + -0.75 = -6.289872813

Reorder the terms:
-0.75 + x = -6.289872813

Solving
-0.75 + x = -6.289872813

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -6.289872813 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -6.289872813 + 0.75
x = -6.289872813 + 0.75

Combine like terms: -6.289872813 + 0.75 = -5.539872813
x = -5.539872813

Simplifying
x = -5.539872813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.039872813, -5.539872813}
Solution
x = {7.039872813, -5.539872813}

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