24x^2-6x-303=0

Solution for 24x^2-6x-303=0 equation:

Simplifying
24x2 + -6x + -303 = 0

Reorder the terms:
-303 + -6x + 24x2 = 0

Solving
-303 + -6x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-101 + -2x + 8x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-101 + -2x + 8x2)' equal to zero and attempt to solve:

Simplifying
-101 + -2x + 8x2 = 0

Solving
-101 + -2x + 8x2 = 0

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

Divide each side by '8'.
-12.625 + -0.25x + x2 = 0

Move the constant term to the right:

Add '12.625' to each side of the equation.
-12.625 + -0.25x + 12.625 + x2 = 0 + 12.625

Reorder the terms:
-12.625 + 12.625 + -0.25x + x2 = 0 + 12.625

Combine like terms: -12.625 + 12.625 = 0.000
0.000 + -0.25x + x2 = 0 + 12.625
-0.25x + x2 = 0 + 12.625

Combine like terms: 0 + 12.625 = 12.625
-0.25x + x2 = 12.625

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 12.625 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 12.625 + 0.015625

Combine like terms: 12.625 + 0.015625 = 12.640625
0.015625 + -0.25x + x2 = 12.640625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 12.640625

Calculate the square root of the right side: 3.555365663

Break this problem into two subproblems by setting 
(x + -0.125) equal to 3.555365663 and -3.555365663.

Subproblem 1
x + -0.125 = 3.555365663

Simplifying
x + -0.125 = 3.555365663

Reorder the terms:
-0.125 + x = 3.555365663

Solving
-0.125 + x = 3.555365663

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 3.555365663 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 3.555365663 + 0.125
x = 3.555365663 + 0.125

Combine like terms: 3.555365663 + 0.125 = 3.680365663
x = 3.680365663

Simplifying
x = 3.680365663

Subproblem 2
x + -0.125 = -3.555365663

Simplifying
x + -0.125 = -3.555365663

Reorder the terms:
-0.125 + x = -3.555365663

Solving
-0.125 + x = -3.555365663

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -3.555365663 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -3.555365663 + 0.125
x = -3.555365663 + 0.125

Combine like terms: -3.555365663 + 0.125 = -3.430365663
x = -3.430365663

Simplifying
x = -3.430365663

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.680365663, -3.430365663}
Solution
x = {3.680365663, -3.430365663}