2a^2-4a-3=0

Solution for 2a^2-4a-3=0 equation:

Simplifying
2a2 + -4a + -3 = 0

Reorder the terms:
-3 + -4a + 2a2 = 0

Solving
-3 + -4a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
-1.5 + -2a + a2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2a + 1.5 + a2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2a + a2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2a + a2 = 0 + 1.5
-2a + a2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2a + a2 = 1.5

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 = 1.5 + 1

Reorder the terms:
1 + -2a + a2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + -2a + a2 = 2.5

Factor a perfect square on the left side:
(a + -1)(a + -1) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(a + -1) equal to 1.58113883 and -1.58113883.

Subproblem 1
a + -1 = 1.58113883

Simplifying
a + -1 = 1.58113883

Reorder the terms:
-1 + a = 1.58113883

Solving
-1 + a = 1.58113883

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 = 1.58113883 + 1

Combine like terms: -1 + 1 = 0
0 + a = 1.58113883 + 1
a = 1.58113883 + 1

Combine like terms: 1.58113883 + 1 = 2.58113883
a = 2.58113883

Simplifying
a = 2.58113883

Subproblem 2
a + -1 = -1.58113883

Simplifying
a + -1 = -1.58113883

Reorder the terms:
-1 + a = -1.58113883

Solving
-1 + a = -1.58113883

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 = -1.58113883 + 1

Combine like terms: -1 + 1 = 0
0 + a = -1.58113883 + 1
a = -1.58113883 + 1

Combine like terms: -1.58113883 + 1 = -0.58113883
a = -0.58113883

Simplifying
a = -0.58113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.58113883, -0.58113883}