(5x^2)-(24x)+6=0

Solution for (5x^2)-(24x)+6=0 equation:

Simplifying
(5x2) + -1(24x) + 6 = 0

Remove parenthesis around (24x)
(5x2) + -1 * 24x + 6 = 0

Multiply -1 * 24
(5x2) + -24x + 6 = 0

Reorder the terms:
6 + -24x + (5x2) = 0

Solving
6 + -24x + (5x2) = 0

Solving for variable 'x'.

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

Divide each side by '5'.
1.2 + -4.8x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -4.8x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -4.8x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -4.8x + x2 = 0 + -1.2
-4.8x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-4.8x + x2 = -1.2

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = -1.2 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = -1.2 + 5.76

Combine like terms: -1.2 + 5.76 = 4.56
5.76 + -4.8x + x2 = 4.56

Factor a perfect square on the left side:
((x) + -2.4)((x) + -2.4) = 4.56

Calculate the square root of the right side: 2.13541565

Break this problem into two subproblems by setting 
((x) + -2.4) equal to 2.13541565 and -2.13541565.

Subproblem 1
(x) + -2.4 = 2.13541565

Simplifying
(x) + -2.4 = 2.13541565
x + -2.4 = 2.13541565

Reorder the terms:
-2.4 + x = 2.13541565

Solving
-2.4 + x = 2.13541565

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = 2.13541565 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 2.13541565 + 2.4
x = 2.13541565 + 2.4

Combine like terms: 2.13541565 + 2.4 = 4.53541565
x = 4.53541565

Simplifying
x = 4.53541565

Subproblem 2
(x) + -2.4 = -2.13541565

Simplifying
(x) + -2.4 = -2.13541565
x + -2.4 = -2.13541565

Reorder the terms:
-2.4 + x = -2.13541565

Solving
-2.4 + x = -2.13541565

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = -2.13541565 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -2.13541565 + 2.4
x = -2.13541565 + 2.4

Combine like terms: -2.13541565 + 2.4 = 0.26458435
x = 0.26458435

Simplifying
x = 0.26458435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.53541565, 0.26458435}