-3x^2-16x+39=0

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Solution for -3x^2-16x+39=0 equation: 


Simplifying
-3x2 + -16x + 39 = 0

Reorder the terms:
39 + -16x + -3x2 = 0

Solving
39 + -16x + -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'.
-13 + 5.333333333x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 5.333333333x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 5.333333333x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 5.333333333x + x2 = 0 + 13
5.333333333x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
5.333333333x + x2 = 13

The x term is 5.333333333x.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333x + 7.111111113 + x2 = 13 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333x + x2 = 13 + 7.111111113

Combine like terms: 13 + 7.111111113 = 20.111111113
7.111111113 + 5.333333333x + x2 = 20.111111113

Factor a perfect square on the left side:
(x + 2.666666667)(x + 2.666666667) = 20.111111113

Calculate the square root of the right side: 4.484541349

Break this problem into two subproblems by setting 
(x + 2.666666667) equal to 4.484541349 and -4.484541349.


Subproblem 1
x + 2.666666667 = 4.484541349

Simplifying
x + 2.666666667 = 4.484541349

Reorder the terms:
2.666666667 + x = 4.484541349

Solving
2.666666667 + x = 4.484541349

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = 4.484541349 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = 4.484541349 + -2.666666667
x = 4.484541349 + -2.666666667

Combine like terms: 4.484541349 + -2.666666667 = 1.817874682
x = 1.817874682

Simplifying
x = 1.817874682


Subproblem 2
x + 2.666666667 = -4.484541349

Simplifying
x + 2.666666667 = -4.484541349

Reorder the terms:
2.666666667 + x = -4.484541349

Solving
2.666666667 + x = -4.484541349

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = -4.484541349 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = -4.484541349 + -2.666666667
x = -4.484541349 + -2.666666667

Combine like terms: -4.484541349 + -2.666666667 = -7.151208016
x = -7.151208016

Simplifying
x = -7.151208016


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.817874682, -7.151208016}

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