2q^2+1=3q-5

Solution for 2q^2+1=3q-5 equation:

Simplifying
2q2 + 1 = 3q + -5

Reorder the terms:
1 + 2q2 = 3q + -5

Reorder the terms:
1 + 2q2 = -5 + 3q

Solving
1 + 2q2 = -5 + 3q

Solving for variable 'q'.

Reorder the terms:
1 + 5 + -3q + 2q2 = -5 + 3q + 5 + -3q

Combine like terms: 1 + 5 = 6
6 + -3q + 2q2 = -5 + 3q + 5 + -3q

Reorder the terms:
6 + -3q + 2q2 = -5 + 5 + 3q + -3q

Combine like terms: -5 + 5 = 0
6 + -3q + 2q2 = 0 + 3q + -3q
6 + -3q + 2q2 = 3q + -3q

Combine like terms: 3q + -3q = 0
6 + -3q + 2q2 = 0

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

Divide each side by '2'.
3 + -1.5q + q2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1.5q + -3 + q2 = 0 + -3

Reorder the terms:
3 + -3 + -1.5q + q2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1.5q + q2 = 0 + -3
-1.5q + q2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1.5q + q2 = -3

The q term is -1.5q.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5q + 0.5625 + q2 = -3 + 0.5625

Reorder the terms:
0.5625 + -1.5q + q2 = -3 + 0.5625

Combine like terms: -3 + 0.5625 = -2.4375
0.5625 + -1.5q + q2 = -2.4375

Factor a perfect square on the left side:
(q + -0.75)(q + -0.75) = -2.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.