826-6q=(4q^2)+159q+228

Solution for 826-6q=(4q^2)+159q+228 equation:

Simplifying
826 + -6q = (4q2) + 159q + 228

Reorder the terms:
826 + -6q = 228 + 159q + (4q2)

Solving
826 + -6q = 228 + 159q + (4q2)

Solving for variable 'q'.

Reorder the terms:
826 + -228 + -6q + -159q + (-4q2) = 228 + 159q + (4q2) + -228 + -159q + (-4q2)

Combine like terms: 826 + -228 = 598
598 + -6q + -159q + (-4q2) = 228 + 159q + (4q2) + -228 + -159q + (-4q2)

Combine like terms: -6q + -159q = -165q
598 + -165q + (-4q2) = 228 + 159q + (4q2) + -228 + -159q + (-4q2)

Reorder the terms:
598 + -165q + (-4q2) = 228 + -228 + 159q + -159q + (4q2) + (-4q2)

Combine like terms: 228 + -228 = 0
598 + -165q + (-4q2) = 0 + 159q + -159q + (4q2) + (-4q2)
598 + -165q + (-4q2) = 159q + -159q + (4q2) + (-4q2)

Combine like terms: 159q + -159q = 0
598 + -165q + (-4q2) = 0 + (4q2) + (-4q2)
598 + -165q + (-4q2) = (4q2) + (-4q2)

Combine like terms: (4q2) + (-4q2) = 0
598 + -165q + (-4q2) = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-149.5 + 41.25q + q2 = 0

Move the constant term to the right:

Add '149.5' to each side of the equation.
-149.5 + 41.25q + 149.5 + q2 = 0 + 149.5

Reorder the terms:
-149.5 + 149.5 + 41.25q + q2 = 0 + 149.5

Combine like terms: -149.5 + 149.5 = 0.0
0.0 + 41.25q + q2 = 0 + 149.5
41.25q + q2 = 0 + 149.5

Combine like terms: 0 + 149.5 = 149.5
41.25q + q2 = 149.5

The q term is 41.25q.  Take half its coefficient (20.625).
Square it (425.390625) and add it to both sides.

Add '425.390625' to each side of the equation.
41.25q + 425.390625 + q2 = 149.5 + 425.390625

Reorder the terms:
425.390625 + 41.25q + q2 = 149.5 + 425.390625

Combine like terms: 149.5 + 425.390625 = 574.890625
425.390625 + 41.25q + q2 = 574.890625

Factor a perfect square on the left side:
((q) + 20.625)((q) + 20.625) = 574.890625

Calculate the square root of the right side: 23.976876882

Break this problem into two subproblems by setting 
((q) + 20.625) equal to 23.976876882 and -23.976876882.

Subproblem 1
(q) + 20.625 = 23.976876882

Simplifying
(q) + 20.625 = 23.976876882
q + 20.625 = 23.976876882

Reorder the terms:
20.625 + q = 23.976876882

Solving
20.625 + q = 23.976876882

Solving for variable 'q'.

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

Add '-20.625' to each side of the equation.
20.625 + -20.625 + q = 23.976876882 + -20.625

Combine like terms: 20.625 + -20.625 = 0.000
0.000 + q = 23.976876882 + -20.625
q = 23.976876882 + -20.625

Combine like terms: 23.976876882 + -20.625 = 3.351876882
q = 3.351876882

Simplifying
q = 3.351876882

Subproblem 2
(q) + 20.625 = -23.976876882

Simplifying
(q) + 20.625 = -23.976876882
q + 20.625 = -23.976876882

Reorder the terms:
20.625 + q = -23.976876882

Solving
20.625 + q = -23.976876882

Solving for variable 'q'.

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

Add '-20.625' to each side of the equation.
20.625 + -20.625 + q = -23.976876882 + -20.625

Combine like terms: 20.625 + -20.625 = 0.000
0.000 + q = -23.976876882 + -20.625
q = -23.976876882 + -20.625

Combine like terms: -23.976876882 + -20.625 = -44.601876882
q = -44.601876882

Simplifying
q = -44.601876882

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {3.351876882, -44.601876882}