3x^2-28x+48=0

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Solution for 3x^2-28x+48=0 equation: 


Simplifying
3x2 + -28x + 48 = 0

Reorder the terms:
48 + -28x + 3x2 = 0

Solving
48 + -28x + 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'.
16 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -9.333333333x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -9.333333333x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -9.333333333x + x2 = 0 + -16
-9.333333333x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-9.333333333x + x2 = -16

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = -16 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = -16 + 21.77777778

Combine like terms: -16 + 21.77777778 = 5.77777778
21.77777778 + -9.333333333x + x2 = 5.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 5.77777778

Calculate the square root of the right side: 2.403700851

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 2.403700851 and -2.403700851.


Subproblem 1
x + -4.666666667 = 2.403700851

Simplifying
x + -4.666666667 = 2.403700851

Reorder the terms:
-4.666666667 + x = 2.403700851

Solving
-4.666666667 + x = 2.403700851

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 2.403700851 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 2.403700851 + 4.666666667
x = 2.403700851 + 4.666666667

Combine like terms: 2.403700851 + 4.666666667 = 7.070367518
x = 7.070367518

Simplifying
x = 7.070367518


Subproblem 2
x + -4.666666667 = -2.403700851

Simplifying
x + -4.666666667 = -2.403700851

Reorder the terms:
-4.666666667 + x = -2.403700851

Solving
-4.666666667 + x = -2.403700851

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -2.403700851 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -2.403700851 + 4.666666667
x = -2.403700851 + 4.666666667

Combine like terms: -2.403700851 + 4.666666667 = 2.262965816
x = 2.262965816

Simplifying
x = 2.262965816


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.070367518, 2.262965816}

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