24x^2-48x+20=0

Solution for 24x^2-48x+20=0 equation:

Simplifying
24x2 + -48x + 20 = 0

Reorder the terms:
20 + -48x + 24x2 = 0

Solving
20 + -48x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -12x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -12x + 6x2)' equal to zero and attempt to solve:

Simplifying
5 + -12x + 6x2 = 0

Solving
5 + -12x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
0.8333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -2x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -2x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.8333333333
-2x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-2x + x2 = -0.8333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.8333333333 + 1

Reorder the terms:
1 + -2x + x2 = -0.8333333333 + 1

Combine like terms: -0.8333333333 + 1 = 0.1666666667
1 + -2x + x2 = 0.1666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.1666666667

Calculate the square root of the right side: 0.408248291

Break this problem into two subproblems by setting 
(x + -1) equal to 0.408248291 and -0.408248291.

Subproblem 1
x + -1 = 0.408248291

Simplifying
x + -1 = 0.408248291

Reorder the terms:
-1 + x = 0.408248291

Solving
-1 + x = 0.408248291

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.408248291 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.408248291 + 1
x = 0.408248291 + 1

Combine like terms: 0.408248291 + 1 = 1.408248291
x = 1.408248291

Simplifying
x = 1.408248291

Subproblem 2
x + -1 = -0.408248291

Simplifying
x + -1 = -0.408248291

Reorder the terms:
-1 + x = -0.408248291

Solving
-1 + x = -0.408248291

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.408248291 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.408248291 + 1
x = -0.408248291 + 1

Combine like terms: -0.408248291 + 1 = 0.591751709
x = 0.591751709

Simplifying
x = 0.591751709

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.408248291, 0.591751709}
Solution
x = {1.408248291, 0.591751709}