3q^2-80q+160=0

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Solution for 3q^2-80q+160=0 equation: 


Simplifying
3q2 + -80q + 160 = 0

Reorder the terms:
160 + -80q + 3q2 = 0

Solving
160 + -80q + 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'.
53.33333333 + -26.66666667q + q2 = 0

Move the constant term to the right:

Add '-53.33333333' to each side of the equation.
53.33333333 + -26.66666667q + -53.33333333 + q2 = 0 + -53.33333333

Reorder the terms:
53.33333333 + -53.33333333 + -26.66666667q + q2 = 0 + -53.33333333

Combine like terms: 53.33333333 + -53.33333333 = 0.00000000
0.00000000 + -26.66666667q + q2 = 0 + -53.33333333
-26.66666667q + q2 = 0 + -53.33333333

Combine like terms: 0 + -53.33333333 = -53.33333333
-26.66666667q + q2 = -53.33333333

The q term is -26.66666667q.  Take half its coefficient (-13.33333334).
Square it (177.7777780) and add it to both sides.

Add '177.7777780' to each side of the equation.
-26.66666667q + 177.7777780 + q2 = -53.33333333 + 177.7777780

Reorder the terms:
177.7777780 + -26.66666667q + q2 = -53.33333333 + 177.7777780

Combine like terms: -53.33333333 + 177.7777780 = 124.44444467
177.7777780 + -26.66666667q + q2 = 124.44444467

Factor a perfect square on the left side:
(q + -13.33333334)(q + -13.33333334) = 124.44444467

Calculate the square root of the right side: 11.155467031

Break this problem into two subproblems by setting 
(q + -13.33333334) equal to 11.155467031 and -11.155467031.


Subproblem 1
q + -13.33333334 = 11.155467031

Simplifying
q + -13.33333334 = 11.155467031

Reorder the terms:
-13.33333334 + q = 11.155467031

Solving
-13.33333334 + q = 11.155467031

Solving for variable 'q'.

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

Add '13.33333334' to each side of the equation.
-13.33333334 + 13.33333334 + q = 11.155467031 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + q = 11.155467031 + 13.33333334
q = 11.155467031 + 13.33333334

Combine like terms: 11.155467031 + 13.33333334 = 24.488800371
q = 24.488800371

Simplifying
q = 24.488800371


Subproblem 2
q + -13.33333334 = -11.155467031

Simplifying
q + -13.33333334 = -11.155467031

Reorder the terms:
-13.33333334 + q = -11.155467031

Solving
-13.33333334 + q = -11.155467031

Solving for variable 'q'.

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

Add '13.33333334' to each side of the equation.
-13.33333334 + 13.33333334 + q = -11.155467031 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + q = -11.155467031 + 13.33333334
q = -11.155467031 + 13.33333334

Combine like terms: -11.155467031 + 13.33333334 = 2.177866309
q = 2.177866309

Simplifying
q = 2.177866309


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {24.488800371, 2.177866309}

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