6a*a-3a+24=0

Solution for 6a*a-3a+24=0 equation:

Simplifying
6a * a + -3a + 24 = 0

Multiply a * a
6a2 + -3a + 24 = 0

Reorder the terms:
24 + -3a + 6a2 = 0

Solving
24 + -3a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -1a + 2a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8 + -1a + 2a2)' equal to zero and attempt to solve:

Simplifying
8 + -1a + 2a2 = 0

Solving
8 + -1a + 2a2 = 0

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

Divide each side by '2'.
4 + -0.5a + a2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -0.5a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + -0.5a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -0.5a + a2 = 0 + -4
-0.5a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
-0.5a + a2 = -4

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = -4 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = -4 + 0.0625

Combine like terms: -4 + 0.0625 = -3.9375
0.0625 + -0.5a + a2 = -3.9375

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = -3.9375

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.