2q^2-8q+6=3

Solution for 2q^2-8q+6=3 equation:

Simplifying
2q2 + -8q + 6 = 3

Reorder the terms:
6 + -8q + 2q2 = 3

Solving
6 + -8q + 2q2 = 3

Solving for variable 'q'.

Reorder the terms:
6 + -3 + -8q + 2q2 = 3 + -3

Combine like terms: 6 + -3 = 3
3 + -8q + 2q2 = 3 + -3

Combine like terms: 3 + -3 = 0
3 + -8q + 2q2 = 0

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

Divide each side by '2'.
1.5 + -4q + q2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -4q + -1.5 + q2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -4q + q2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -4q + q2 = 0 + -1.5
-4q + q2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-4q + q2 = -1.5

The q term is -4q.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4q + 4 + q2 = -1.5 + 4

Reorder the terms:
4 + -4q + q2 = -1.5 + 4

Combine like terms: -1.5 + 4 = 2.5
4 + -4q + q2 = 2.5

Factor a perfect square on the left side:
(q + -2)(q + -2) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(q + -2) equal to 1.58113883 and -1.58113883.

Subproblem 1
q + -2 = 1.58113883

Simplifying
q + -2 = 1.58113883

Reorder the terms:
-2 + q = 1.58113883

Solving
-2 + q = 1.58113883

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = 1.58113883 + 2

Combine like terms: -2 + 2 = 0
0 + q = 1.58113883 + 2
q = 1.58113883 + 2

Combine like terms: 1.58113883 + 2 = 3.58113883
q = 3.58113883

Simplifying
q = 3.58113883

Subproblem 2
q + -2 = -1.58113883

Simplifying
q + -2 = -1.58113883

Reorder the terms:
-2 + q = -1.58113883

Solving
-2 + q = -1.58113883

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = -1.58113883 + 2

Combine like terms: -2 + 2 = 0
0 + q = -1.58113883 + 2
q = -1.58113883 + 2

Combine like terms: -1.58113883 + 2 = 0.41886117
q = 0.41886117

Simplifying
q = 0.41886117

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {3.58113883, 0.41886117}