-3q^2+780q-11=0

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Solution for -3q^2+780q-11=0 equation: 


Simplifying
-3q2 + 780q + -11 = 0

Reorder the terms:
-11 + 780q + -3q2 = 0

Solving
-11 + 780q + -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'.
3.666666667 + -260q + q2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -260q + -3.666666667 + q2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -260q + q2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -260q + q2 = 0 + -3.666666667
-260q + q2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-260q + q2 = -3.666666667

The q term is -260q.  Take half its coefficient (-130).
Square it (16900) and add it to both sides.

Add '16900' to each side of the equation.
-260q + 16900 + q2 = -3.666666667 + 16900

Reorder the terms:
16900 + -260q + q2 = -3.666666667 + 16900

Combine like terms: -3.666666667 + 16900 = 16896.333333333
16900 + -260q + q2 = 16896.333333333

Factor a perfect square on the left side:
(q + -130)(q + -130) = 16896.333333333

Calculate the square root of the right side: 129.985896671

Break this problem into two subproblems by setting 
(q + -130) equal to 129.985896671 and -129.985896671.


Subproblem 1
q + -130 = 129.985896671

Simplifying
q + -130 = 129.985896671

Reorder the terms:
-130 + q = 129.985896671

Solving
-130 + q = 129.985896671

Solving for variable 'q'.

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

Add '130' to each side of the equation.
-130 + 130 + q = 129.985896671 + 130

Combine like terms: -130 + 130 = 0
0 + q = 129.985896671 + 130
q = 129.985896671 + 130

Combine like terms: 129.985896671 + 130 = 259.985896671
q = 259.985896671

Simplifying
q = 259.985896671


Subproblem 2
q + -130 = -129.985896671

Simplifying
q + -130 = -129.985896671

Reorder the terms:
-130 + q = -129.985896671

Solving
-130 + q = -129.985896671

Solving for variable 'q'.

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

Add '130' to each side of the equation.
-130 + 130 + q = -129.985896671 + 130

Combine like terms: -130 + 130 = 0
0 + q = -129.985896671 + 130
q = -129.985896671 + 130

Combine like terms: -129.985896671 + 130 = 0.014103329
q = 0.014103329

Simplifying
q = 0.014103329


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {259.985896671, 0.014103329}

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