0=8-12Q+3Q^2

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Solution for 0=8-12Q+3Q^2 equation: 


Simplifying
0 = 8 + -12Q + 3Q2

Solving
0 = 8 + -12Q + 3Q2

Solving for variable 'Q'.

Combine like terms: 0 + -8 = -8
-8 + 12Q + -3Q2 = 8 + -12Q + 3Q2 + -8 + 12Q + -3Q2

Reorder the terms:
-8 + 12Q + -3Q2 = 8 + -8 + -12Q + 12Q + 3Q2 + -3Q2

Combine like terms: 8 + -8 = 0
-8 + 12Q + -3Q2 = 0 + -12Q + 12Q + 3Q2 + -3Q2
-8 + 12Q + -3Q2 = -12Q + 12Q + 3Q2 + -3Q2

Combine like terms: -12Q + 12Q = 0
-8 + 12Q + -3Q2 = 0 + 3Q2 + -3Q2
-8 + 12Q + -3Q2 = 3Q2 + -3Q2

Combine like terms: 3Q2 + -3Q2 = 0
-8 + 12Q + -3Q2 = 0

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

Divide each side by '-3'.
2.666666667 + -4Q + Q2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -4Q + -2.666666667 + Q2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -4Q + Q2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -4Q + Q2 = 0 + -2.666666667
-4Q + Q2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-4Q + Q2 = -2.666666667

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 = -2.666666667 + 4

Reorder the terms:
4 + -4Q + Q2 = -2.666666667 + 4

Combine like terms: -2.666666667 + 4 = 1.333333333
4 + -4Q + Q2 = 1.333333333

Factor a perfect square on the left side:
(Q + -2)(Q + -2) = 1.333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(Q + -2) equal to 1.154700538 and -1.154700538.


Subproblem 1
Q + -2 = 1.154700538

Simplifying
Q + -2 = 1.154700538

Reorder the terms:
-2 + Q = 1.154700538

Solving
-2 + Q = 1.154700538

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 = 1.154700538 + 2

Combine like terms: -2 + 2 = 0
0 + Q = 1.154700538 + 2
Q = 1.154700538 + 2

Combine like terms: 1.154700538 + 2 = 3.154700538
Q = 3.154700538

Simplifying
Q = 3.154700538


Subproblem 2
Q + -2 = -1.154700538

Simplifying
Q + -2 = -1.154700538

Reorder the terms:
-2 + Q = -1.154700538

Solving
-2 + Q = -1.154700538

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 = -1.154700538 + 2

Combine like terms: -2 + 2 = 0
0 + Q = -1.154700538 + 2
Q = -1.154700538 + 2

Combine like terms: -1.154700538 + 2 = 0.845299462
Q = 0.845299462

Simplifying
Q = 0.845299462


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {3.154700538, 0.845299462}

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