9q^2+2q-3=0

Solution for 9q^2+2q-3=0 equation:

Simplifying
9q2 + 2q + -3 = 0

Reorder the terms:
-3 + 2q + 9q2 = 0

Solving
-3 + 2q + 9q2 = 0

Solving for variable 'q'.

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

Divide each side by '9'.
-0.3333333333 + 0.2222222222q + q2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.2222222222q + 0.3333333333 + q2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.2222222222q + q2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.2222222222q + q2 = 0 + 0.3333333333
0.2222222222q + q2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.2222222222q + q2 = 0.3333333333

The q term is 0.2222222222q.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222q + 0.01234567901 + q2 = 0.3333333333 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222q + q2 = 0.3333333333 + 0.01234567901

Combine like terms: 0.3333333333 + 0.01234567901 = 0.34567901231
0.01234567901 + 0.2222222222q + q2 = 0.34567901231

Factor a perfect square on the left side:
(q + 0.1111111111)(q + 0.1111111111) = 0.34567901231

Calculate the square root of the right side: 0.587944736

Break this problem into two subproblems by setting 
(q + 0.1111111111) equal to 0.587944736 and -0.587944736.

Subproblem 1
q + 0.1111111111 = 0.587944736

Simplifying
q + 0.1111111111 = 0.587944736

Reorder the terms:
0.1111111111 + q = 0.587944736

Solving
0.1111111111 + q = 0.587944736

Solving for variable 'q'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + q = 0.587944736 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + q = 0.587944736 + -0.1111111111
q = 0.587944736 + -0.1111111111

Combine like terms: 0.587944736 + -0.1111111111 = 0.4768336249
q = 0.4768336249

Simplifying
q = 0.4768336249

Subproblem 2
q + 0.1111111111 = -0.587944736

Simplifying
q + 0.1111111111 = -0.587944736

Reorder the terms:
0.1111111111 + q = -0.587944736

Solving
0.1111111111 + q = -0.587944736

Solving for variable 'q'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + q = -0.587944736 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + q = -0.587944736 + -0.1111111111
q = -0.587944736 + -0.1111111111

Combine like terms: -0.587944736 + -0.1111111111 = -0.6990558471
q = -0.6990558471

Simplifying
q = -0.6990558471

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.4768336249, -0.6990558471}