3a^2-6a-5=0

Solution for 3a^2-6a-5=0 equation:

Simplifying
3a2 + -6a + -5 = 0

Reorder the terms:
-5 + -6a + 3a2 = 0

Solving
-5 + -6a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-1.666666667 + -2a + a2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -2a + 1.666666667 + a2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -2a + a2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -2a + a2 = 0 + 1.666666667
-2a + a2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-2a + a2 = 1.666666667

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 1.666666667 + 1

Reorder the terms:
1 + -2a + a2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + -2a + a2 = 2.666666667

Factor a perfect square on the left side:
(a + -1)(a + -1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(a + -1) equal to 1.632993162 and -1.632993162.

Subproblem 1
a + -1 = 1.632993162

Simplifying
a + -1 = 1.632993162

Reorder the terms:
-1 + a = 1.632993162

Solving
-1 + a = 1.632993162

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + a = 1.632993162 + 1
a = 1.632993162 + 1

Combine like terms: 1.632993162 + 1 = 2.632993162
a = 2.632993162

Simplifying
a = 2.632993162

Subproblem 2
a + -1 = -1.632993162

Simplifying
a + -1 = -1.632993162

Reorder the terms:
-1 + a = -1.632993162

Solving
-1 + a = -1.632993162

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + a = -1.632993162 + 1
a = -1.632993162 + 1

Combine like terms: -1.632993162 + 1 = -0.632993162
a = -0.632993162

Simplifying
a = -0.632993162

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.632993162, -0.632993162}