0=5q-(8+2q^2)

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Solution for 0=5q-(8+2q^2) equation: 


Simplifying
0 = 5q + -1(8 + 2q2)
0 = 5q + (8 * -1 + 2q2 * -1)
0 = 5q + (-8 + -2q2)

Reorder the terms:
0 = -8 + 5q + -2q2

Solving
0 = -8 + 5q + -2q2

Solving for variable 'q'.

Combine like terms: 0 + 8 = 8
8 + -5q + 2q2 = -8 + 5q + -2q2 + 8 + -5q + 2q2

Reorder the terms:
8 + -5q + 2q2 = -8 + 8 + 5q + -5q + -2q2 + 2q2

Combine like terms: -8 + 8 = 0
8 + -5q + 2q2 = 0 + 5q + -5q + -2q2 + 2q2
8 + -5q + 2q2 = 5q + -5q + -2q2 + 2q2

Combine like terms: 5q + -5q = 0
8 + -5q + 2q2 = 0 + -2q2 + 2q2
8 + -5q + 2q2 = -2q2 + 2q2

Combine like terms: -2q2 + 2q2 = 0
8 + -5q + 2q2 = 0

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

Divide each side by '2'.
4 + -2.5q + q2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -2.5q + -4 + q2 = 0 + -4

Reorder the terms:
4 + -4 + -2.5q + q2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2.5q + q2 = 0 + -4
-2.5q + q2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2.5q + q2 = -4

The q term is -2.5q.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5q + 1.5625 + q2 = -4 + 1.5625

Reorder the terms:
1.5625 + -2.5q + q2 = -4 + 1.5625

Combine like terms: -4 + 1.5625 = -2.4375
1.5625 + -2.5q + q2 = -2.4375

Factor a perfect square on the left side:
(q + -1.25)(q + -1.25) = -2.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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