86-6q-3q^2=0

Solution for 86-6q-3q^2=0 equation:

Simplifying
86 + -6q + -3q2 = 0

Solving
86 + -6q + -3q2 = 0

Solving for variable 'q'.

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

Divide each side by '-3'.
-28.66666667 + 2q + q2 = 0

Move the constant term to the right:

Add '28.66666667' to each side of the equation.
-28.66666667 + 2q + 28.66666667 + q2 = 0 + 28.66666667

Reorder the terms:
-28.66666667 + 28.66666667 + 2q + q2 = 0 + 28.66666667

Combine like terms: -28.66666667 + 28.66666667 = 0.00000000
0.00000000 + 2q + q2 = 0 + 28.66666667
2q + q2 = 0 + 28.66666667

Combine like terms: 0 + 28.66666667 = 28.66666667
2q + q2 = 28.66666667

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 = 28.66666667 + 1

Reorder the terms:
1 + 2q + q2 = 28.66666667 + 1

Combine like terms: 28.66666667 + 1 = 29.66666667
1 + 2q + q2 = 29.66666667

Factor a perfect square on the left side:
(q + 1)(q + 1) = 29.66666667

Calculate the square root of the right side: 5.446711546

Break this problem into two subproblems by setting 
(q + 1) equal to 5.446711546 and -5.446711546.

Subproblem 1
q + 1 = 5.446711546

Simplifying
q + 1 = 5.446711546

Reorder the terms:
1 + q = 5.446711546

Solving
1 + q = 5.446711546

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 = 5.446711546 + -1

Combine like terms: 1 + -1 = 0
0 + q = 5.446711546 + -1
q = 5.446711546 + -1

Combine like terms: 5.446711546 + -1 = 4.446711546
q = 4.446711546

Simplifying
q = 4.446711546

Subproblem 2
q + 1 = -5.446711546

Simplifying
q + 1 = -5.446711546

Reorder the terms:
1 + q = -5.446711546

Solving
1 + q = -5.446711546

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 = -5.446711546 + -1

Combine like terms: 1 + -1 = 0
0 + q = -5.446711546 + -1
q = -5.446711546 + -1

Combine like terms: -5.446711546 + -1 = -6.446711546
q = -6.446711546

Simplifying
q = -6.446711546

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4.446711546, -6.446711546}