3x^2-24x+39=0

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Solution for 3x^2-24x+39=0 equation: 


Simplifying
3x2 + -24x + 39 = 0

Reorder the terms:
39 + -24x + 3x2 = 0

Solving
39 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(13 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(13 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
13 + -8x + x2 = 0

Solving
13 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -8x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -8x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -8x + x2 = 0 + -13
-8x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-8x + x2 = -13

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -13 + 16

Reorder the terms:
16 + -8x + x2 = -13 + 16

Combine like terms: -13 + 16 = 3
16 + -8x + x2 = 3

Factor a perfect square on the left side:
(x + -4)(x + -4) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -4) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -4 = 1.732050808

Simplifying
x + -4 = 1.732050808

Reorder the terms:
-4 + x = 1.732050808

Solving
-4 + x = 1.732050808

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 1.732050808 + 4

Combine like terms: -4 + 4 = 0
0 + x = 1.732050808 + 4
x = 1.732050808 + 4

Combine like terms: 1.732050808 + 4 = 5.732050808
x = 5.732050808

Simplifying
x = 5.732050808


Subproblem 2
x + -4 = -1.732050808

Simplifying
x + -4 = -1.732050808

Reorder the terms:
-4 + x = -1.732050808

Solving
-4 + x = -1.732050808

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -1.732050808 + 4

Combine like terms: -4 + 4 = 0
0 + x = -1.732050808 + 4
x = -1.732050808 + 4

Combine like terms: -1.732050808 + 4 = 2.267949192
x = 2.267949192

Simplifying
x = 2.267949192


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.732050808, 2.267949192}
Solution
x = {5.732050808, 2.267949192}

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