2q^2+4q-3=0

Solution for 2q^2+4q-3=0 equation:

Simplifying
2q2 + 4q + -3 = 0

Reorder the terms:
-3 + 4q + 2q2 = 0

Solving
-3 + 4q + 2q2 = 0

Solving for variable 'q'.

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

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

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2q + 1.5 + q2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2q + q2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2q + q2 = 0 + 1.5
2q + q2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2q + q2 = 1.5

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

Add '1' to each side of the equation.
2q + 1 + q2 = 1.5 + 1

Reorder the terms:
1 + 2q + q2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + 2q + q2 = 2.5

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

Calculate the square root of the right side: 1.58113883

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

Subproblem 1
q + 1 = 1.58113883

Simplifying
q + 1 = 1.58113883

Reorder the terms:
1 + q = 1.58113883

Solving
1 + q = 1.58113883

Solving for variable 'q'.

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

Add '-1' to each side of the equation.
1 + -1 + q = 1.58113883 + -1

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

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

Simplifying
q = 0.58113883

Subproblem 2
q + 1 = -1.58113883

Simplifying
q + 1 = -1.58113883

Reorder the terms:
1 + q = -1.58113883

Solving
1 + q = -1.58113883

Solving for variable 'q'.

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

Add '-1' to each side of the equation.
1 + -1 + q = -1.58113883 + -1

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

Combine like terms: -1.58113883 + -1 = -2.58113883
q = -2.58113883

Simplifying
q = -2.58113883

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