8a^2=2a-6

Solution for 8a^2=2a-6 equation:

Simplifying
8a2 = 2a + -6

Reorder the terms:
8a2 = -6 + 2a

Solving
8a2 = -6 + 2a

Solving for variable 'a'.

Reorder the terms:
6 + -2a + 8a2 = -6 + 2a + 6 + -2a

Reorder the terms:
6 + -2a + 8a2 = -6 + 6 + 2a + -2a

Combine like terms: -6 + 6 = 0
6 + -2a + 8a2 = 0 + 2a + -2a
6 + -2a + 8a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
6 + -2a + 8a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -1a + 4a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1a + 4a2)' equal to zero and attempt to solve:

Simplifying
3 + -1a + 4a2 = 0

Solving
3 + -1a + 4a2 = 0

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

Divide each side by '4'.
0.75 + -0.25a + a2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -0.25a + -0.75 + a2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -0.25a + a2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -0.25a + a2 = 0 + -0.75
-0.25a + a2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-0.25a + a2 = -0.75

The a term is -0.25a.  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.
-0.25a + 0.015625 + a2 = -0.75 + 0.015625

Reorder the terms:
0.015625 + -0.25a + a2 = -0.75 + 0.015625

Combine like terms: -0.75 + 0.015625 = -0.734375
0.015625 + -0.25a + a2 = -0.734375

Factor a perfect square on the left side:
(a + -0.125)(a + -0.125) = -0.734375

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.