1.5x^2-8.5x-39=0

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Solution for 1.5x^2-8.5x-39=0 equation: 


Simplifying
1.5x2 + -8.5x + -39 = 0

Reorder the terms:
-39 + -8.5x + 1.5x2 = 0

Solving
-39 + -8.5x + 1.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.5'.
-26 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -5.666666667x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -5.666666667x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -5.666666667x + x2 = 0 + 26
-5.666666667x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-5.666666667x + x2 = 26

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 26 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 26 + 8.027777782

Combine like terms: 26 + 8.027777782 = 34.027777782
8.027777782 + -5.666666667x + x2 = 34.027777782

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 34.027777782

Calculate the square root of the right side: 5.833333334

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 5.833333334 and -5.833333334.


Subproblem 1
x + -2.833333334 = 5.833333334

Simplifying
x + -2.833333334 = 5.833333334

Reorder the terms:
-2.833333334 + x = 5.833333334

Solving
-2.833333334 + x = 5.833333334

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 5.833333334 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 5.833333334 + 2.833333334
x = 5.833333334 + 2.833333334

Combine like terms: 5.833333334 + 2.833333334 = 8.666666668
x = 8.666666668

Simplifying
x = 8.666666668


Subproblem 2
x + -2.833333334 = -5.833333334

Simplifying
x + -2.833333334 = -5.833333334

Reorder the terms:
-2.833333334 + x = -5.833333334

Solving
-2.833333334 + x = -5.833333334

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -5.833333334 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -5.833333334 + 2.833333334
x = -5.833333334 + 2.833333334

Combine like terms: -5.833333334 + 2.833333334 = -3
x = -3

Simplifying
x = -3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.666666668, -3}

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