24x^2-8x+72=0

Solution for 24x^2-8x+72=0 equation:

Simplifying
24x2 + -8x + 72 = 0

Reorder the terms:
72 + -8x + 24x2 = 0

Solving
72 + -8x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(9 + -1x + 3x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(9 + -1x + 3x2)' equal to zero and attempt to solve:

Simplifying
9 + -1x + 3x2 = 0

Solving
9 + -1x + 3x2 = 0

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

Divide each side by '3'.
3 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -0.3333333333x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -0.3333333333x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -0.3333333333x + x2 = 0 + -3
-0.3333333333x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-0.3333333333x + x2 = -3

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = -3 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = -3 + 0.02777777779

Combine like terms: -3 + 0.02777777779 = -2.97222222221
0.02777777779 + -0.3333333333x + x2 = -2.97222222221

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = -2.97222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.