0.24x^2-2.4x+6=0

Solution for 0.24x^2-2.4x+6=0 equation:

Simplifying
0.24x2 + -2.4x + 6 = 0

Reorder the terms:
6 + -2.4x + 0.24x2 = 0

Solving
6 + -2.4x + 0.24x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.24'.
25 + -10x + x2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -10x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -10x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -10x + x2 = 0 + -25
-10x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-10x + x2 = -25

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -25 + 25

Reorder the terms:
25 + -10x + x2 = -25 + 25

Combine like terms: -25 + 25 = 0
25 + -10x + x2 = 0

Factor a perfect square on the left side:
(x + -5)(x + -5) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -5) equal to 0 and 0.

Subproblem 1
x + -5 = 0

Simplifying
x + -5 = 0

Reorder the terms:
-5 + x = 0

Solving
-5 + x = 0

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

Subproblem 2
x + -5 = 0

Simplifying
x + -5 = 0

Reorder the terms:
-5 + x = 0

Solving
-5 + x = 0

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, 5}