3q^2-80q+170=0

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Solution for 3q^2-80q+170=0 equation: 


Simplifying
3q2 + -80q + 170 = 0

Reorder the terms:
170 + -80q + 3q2 = 0

Solving
170 + -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'.
56.66666667 + -26.66666667q + q2 = 0

Move the constant term to the right:

Add '-56.66666667' to each side of the equation.
56.66666667 + -26.66666667q + -56.66666667 + q2 = 0 + -56.66666667

Reorder the terms:
56.66666667 + -56.66666667 + -26.66666667q + q2 = 0 + -56.66666667

Combine like terms: 56.66666667 + -56.66666667 = 0.00000000
0.00000000 + -26.66666667q + q2 = 0 + -56.66666667
-26.66666667q + q2 = 0 + -56.66666667

Combine like terms: 0 + -56.66666667 = -56.66666667
-26.66666667q + q2 = -56.66666667

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 = -56.66666667 + 177.7777780

Reorder the terms:
177.7777780 + -26.66666667q + q2 = -56.66666667 + 177.7777780

Combine like terms: -56.66666667 + 177.7777780 = 121.11111133
177.7777780 + -26.66666667q + q2 = 121.11111133

Factor a perfect square on the left side:
(q + -13.33333334)(q + -13.33333334) = 121.11111133

Calculate the square root of the right side: 11.005049356

Break this problem into two subproblems by setting 
(q + -13.33333334) equal to 11.005049356 and -11.005049356.


Subproblem 1
q + -13.33333334 = 11.005049356

Simplifying
q + -13.33333334 = 11.005049356

Reorder the terms:
-13.33333334 + q = 11.005049356

Solving
-13.33333334 + q = 11.005049356

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 = 11.005049356 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + q = 11.005049356 + 13.33333334
q = 11.005049356 + 13.33333334

Combine like terms: 11.005049356 + 13.33333334 = 24.338382696
q = 24.338382696

Simplifying
q = 24.338382696


Subproblem 2
q + -13.33333334 = -11.005049356

Simplifying
q + -13.33333334 = -11.005049356

Reorder the terms:
-13.33333334 + q = -11.005049356

Solving
-13.33333334 + q = -11.005049356

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 = -11.005049356 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + q = -11.005049356 + 13.33333334
q = -11.005049356 + 13.33333334

Combine like terms: -11.005049356 + 13.33333334 = 2.328283984
q = 2.328283984

Simplifying
q = 2.328283984


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {24.338382696, 2.328283984}

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