4x^2-84x+24=0

Solution for 4x^2-84x+24=0 equation:

Simplifying
4x2 + -84x + 24 = 0

Reorder the terms:
24 + -84x + 4x2 = 0

Solving
24 + -84x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -21x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + -21x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -21x + x2 = 0

Solving
6 + -21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -21x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -21x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -21x + x2 = 0 + -6
-21x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-21x + x2 = -6

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -6 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -6 + 110.25

Combine like terms: -6 + 110.25 = 104.25
110.25 + -21x + x2 = 104.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 104.25

Calculate the square root of the right side: 10.210288928

Break this problem into two subproblems by setting 
(x + -10.5) equal to 10.210288928 and -10.210288928.

Subproblem 1
x + -10.5 = 10.210288928

Simplifying
x + -10.5 = 10.210288928

Reorder the terms:
-10.5 + x = 10.210288928

Solving
-10.5 + x = 10.210288928

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 10.210288928 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 10.210288928 + 10.5
x = 10.210288928 + 10.5

Combine like terms: 10.210288928 + 10.5 = 20.710288928
x = 20.710288928

Simplifying
x = 20.710288928

Subproblem 2
x + -10.5 = -10.210288928

Simplifying
x + -10.5 = -10.210288928

Reorder the terms:
-10.5 + x = -10.210288928

Solving
-10.5 + x = -10.210288928

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -10.210288928 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -10.210288928 + 10.5
x = -10.210288928 + 10.5

Combine like terms: -10.210288928 + 10.5 = 0.289711072
x = 0.289711072

Simplifying
x = 0.289711072

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.710288928, 0.289711072}
Solution
x = {20.710288928, 0.289711072}