(3x^2)-12x-92=0

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Solution for (3x^2)-12x-92=0 equation: 


Simplifying
(3x2) + -12x + -92 = 0

Reorder the terms:
-92 + -12x + (3x2) = 0

Solving
-92 + -12x + (3x2) = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-30.66666667 + -4x + x2 = 0

Move the constant term to the right:

Add '30.66666667' to each side of the equation.
-30.66666667 + -4x + 30.66666667 + x2 = 0 + 30.66666667

Reorder the terms:
-30.66666667 + 30.66666667 + -4x + x2 = 0 + 30.66666667

Combine like terms: -30.66666667 + 30.66666667 = 0.00000000
0.00000000 + -4x + x2 = 0 + 30.66666667
-4x + x2 = 0 + 30.66666667

Combine like terms: 0 + 30.66666667 = 30.66666667
-4x + x2 = 30.66666667

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 30.66666667 + 4

Reorder the terms:
4 + -4x + x2 = 30.66666667 + 4

Combine like terms: 30.66666667 + 4 = 34.66666667
4 + -4x + x2 = 34.66666667

Factor a perfect square on the left side:
((x) + -2)((x) + -2) = 34.66666667

Calculate the square root of the right side: 5.887840578

Break this problem into two subproblems by setting 
((x) + -2) equal to 5.887840578 and -5.887840578.


Subproblem 1
(x) + -2 = 5.887840578

Simplifying
(x) + -2 = 5.887840578
x + -2 = 5.887840578

Reorder the terms:
-2 + x = 5.887840578

Solving
-2 + x = 5.887840578

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 5.887840578 + 2

Combine like terms: -2 + 2 = 0
0 + x = 5.887840578 + 2
x = 5.887840578 + 2

Combine like terms: 5.887840578 + 2 = 7.887840578
x = 7.887840578

Simplifying
x = 7.887840578


Subproblem 2
(x) + -2 = -5.887840578

Simplifying
(x) + -2 = -5.887840578
x + -2 = -5.887840578

Reorder the terms:
-2 + x = -5.887840578

Solving
-2 + x = -5.887840578

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -5.887840578 + 2

Combine like terms: -2 + 2 = 0
0 + x = -5.887840578 + 2
x = -5.887840578 + 2

Combine like terms: -5.887840578 + 2 = -3.887840578
x = -3.887840578

Simplifying
x = -3.887840578


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.887840578, -3.887840578}

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