3x^2-48x+64=0

Solution for 3x^2-48x+64=0 equation:

Simplifying
3x2 + -48x + 64 = 0

Reorder the terms:
64 + -48x + 3x2 = 0

Solving
64 + -48x + 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'.
21.33333333 + -16x + x2 = 0

Move the constant term to the right:

Add '-21.33333333' to each side of the equation.
21.33333333 + -16x + -21.33333333 + x2 = 0 + -21.33333333

Reorder the terms:
21.33333333 + -21.33333333 + -16x + x2 = 0 + -21.33333333

Combine like terms: 21.33333333 + -21.33333333 = 0.00000000
0.00000000 + -16x + x2 = 0 + -21.33333333
-16x + x2 = 0 + -21.33333333

Combine like terms: 0 + -21.33333333 = -21.33333333
-16x + x2 = -21.33333333

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 = -21.33333333 + 64

Reorder the terms:
64 + -16x + x2 = -21.33333333 + 64

Combine like terms: -21.33333333 + 64 = 42.66666667
64 + -16x + x2 = 42.66666667

Factor a perfect square on the left side:
(x + -8)(x + -8) = 42.66666667

Calculate the square root of the right side: 6.531972648

Break this problem into two subproblems by setting 
(x + -8) equal to 6.531972648 and -6.531972648.

Subproblem 1
x + -8 = 6.531972648

Simplifying
x + -8 = 6.531972648

Reorder the terms:
-8 + x = 6.531972648

Solving
-8 + x = 6.531972648

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 = 6.531972648 + 8

Combine like terms: -8 + 8 = 0
0 + x = 6.531972648 + 8
x = 6.531972648 + 8

Combine like terms: 6.531972648 + 8 = 14.531972648
x = 14.531972648

Simplifying
x = 14.531972648

Subproblem 2
x + -8 = -6.531972648

Simplifying
x + -8 = -6.531972648

Reorder the terms:
-8 + x = -6.531972648

Solving
-8 + x = -6.531972648

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 = -6.531972648 + 8

Combine like terms: -8 + 8 = 0
0 + x = -6.531972648 + 8
x = -6.531972648 + 8

Combine like terms: -6.531972648 + 8 = 1.468027352
x = 1.468027352

Simplifying
x = 1.468027352

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.531972648, 1.468027352}