12a^2-17a-6=0

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Solution for 12a^2-17a-6=0 equation:


Simplifying
12a2 + -17a + -6 = 0

Reorder the terms:
-6 + -17a + 12a2 = 0

Solving
-6 + -17a + 12a2 = 0

Solving for variable 'a'.

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

Divide each side by '12'.
-0.5 + -1.416666667a + a2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.416666667a + 0.5 + a2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.416666667a + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.416666667a + a2 = 0 + 0.5
-1.416666667a + a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.416666667a + a2 = 0.5

The a term is -1.416666667a.  Take half its coefficient (-0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
-1.416666667a + 0.5017361113 + a2 = 0.5 + 0.5017361113

Reorder the terms:
0.5017361113 + -1.416666667a + a2 = 0.5 + 0.5017361113

Combine like terms: 0.5 + 0.5017361113 = 1.0017361113
0.5017361113 + -1.416666667a + a2 = 1.0017361113

Factor a perfect square on the left side:
(a + -0.7083333335)(a + -0.7083333335) = 1.0017361113

Calculate the square root of the right side: 1.000867679

Break this problem into two subproblems by setting 
(a + -0.7083333335) equal to 1.000867679 and -1.000867679.

Subproblem 1

a + -0.7083333335 = 1.000867679 Simplifying a + -0.7083333335 = 1.000867679 Reorder the terms: -0.7083333335 + a = 1.000867679 Solving -0.7083333335 + a = 1.000867679 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + a = 1.000867679 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + a = 1.000867679 + 0.7083333335 a = 1.000867679 + 0.7083333335 Combine like terms: 1.000867679 + 0.7083333335 = 1.7092010125 a = 1.7092010125 Simplifying a = 1.7092010125

Subproblem 2

a + -0.7083333335 = -1.000867679 Simplifying a + -0.7083333335 = -1.000867679 Reorder the terms: -0.7083333335 + a = -1.000867679 Solving -0.7083333335 + a = -1.000867679 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + a = -1.000867679 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + a = -1.000867679 + 0.7083333335 a = -1.000867679 + 0.7083333335 Combine like terms: -1.000867679 + 0.7083333335 = -0.2925343455 a = -0.2925343455 Simplifying a = -0.2925343455

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.7092010125, -0.2925343455}

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