3x^2-48x+39=0

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Solution for 3x^2-48x+39=0 equation: 


Simplifying
3x2 + -48x + 39 = 0

Reorder the terms:
39 + -48x + 3x2 = 0

Solving
39 + -48x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(13 + -16x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(13 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
13 + -16x + x2 = 0

Solving
13 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -16x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -16x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -16x + x2 = 0 + -13
-16x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-16x + x2 = -13

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -13 + 64

Reorder the terms:
64 + -16x + x2 = -13 + 64

Combine like terms: -13 + 64 = 51
64 + -16x + x2 = 51

Factor a perfect square on the left side:
(x + -8)(x + -8) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + -8) equal to 7.141428429 and -7.141428429.


Subproblem 1
x + -8 = 7.141428429

Simplifying
x + -8 = 7.141428429

Reorder the terms:
-8 + x = 7.141428429

Solving
-8 + x = 7.141428429

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 7.141428429 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.141428429 + 8
x = 7.141428429 + 8

Combine like terms: 7.141428429 + 8 = 15.141428429
x = 15.141428429

Simplifying
x = 15.141428429


Subproblem 2
x + -8 = -7.141428429

Simplifying
x + -8 = -7.141428429

Reorder the terms:
-8 + x = -7.141428429

Solving
-8 + x = -7.141428429

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -7.141428429 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.141428429 + 8
x = -7.141428429 + 8

Combine like terms: -7.141428429 + 8 = 0.858571571
x = 0.858571571

Simplifying
x = 0.858571571


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.141428429, 0.858571571}
Solution
x = {15.141428429, 0.858571571}

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