6a^2-17a-12=0

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


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

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

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

Solving for variable 'a'.

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

Divide each side by '6'.
-2 + -2.833333333a + a2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2.833333333a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + -2.833333333a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2.833333333a + a2 = 0 + 2
-2.833333333a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2.833333333a + a2 = 2

The a term is -2.833333333a.  Take half its coefficient (-1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
-2.833333333a + 2.006944445 + a2 = 2 + 2.006944445

Reorder the terms:
2.006944445 + -2.833333333a + a2 = 2 + 2.006944445

Combine like terms: 2 + 2.006944445 = 4.006944445
2.006944445 + -2.833333333a + a2 = 4.006944445

Factor a perfect square on the left side:
(a + -1.416666667)(a + -1.416666667) = 4.006944445

Calculate the square root of the right side: 2.001735358

Break this problem into two subproblems by setting 
(a + -1.416666667) equal to 2.001735358 and -2.001735358.


Subproblem 1
a + -1.416666667 = 2.001735358

Simplifying
a + -1.416666667 = 2.001735358

Reorder the terms:
-1.416666667 + a = 2.001735358

Solving
-1.416666667 + a = 2.001735358

Solving for variable 'a'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + a = 2.001735358 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + a = 2.001735358 + 1.416666667
a = 2.001735358 + 1.416666667

Combine like terms: 2.001735358 + 1.416666667 = 3.418402025
a = 3.418402025

Simplifying
a = 3.418402025


Subproblem 2
a + -1.416666667 = -2.001735358

Simplifying
a + -1.416666667 = -2.001735358

Reorder the terms:
-1.416666667 + a = -2.001735358

Solving
-1.416666667 + a = -2.001735358

Solving for variable 'a'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + a = -2.001735358 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + a = -2.001735358 + 1.416666667
a = -2.001735358 + 1.416666667

Combine like terms: -2.001735358 + 1.416666667 = -0.585068691
a = -0.585068691

Simplifying
a = -0.585068691


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.418402025, -0.585068691}

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