2q^2+4q=7q^2+1

Solution for 2q^2+4q=7q^2+1 equation:

Simplifying
2q2 + 4q = 7q2 + 1

Reorder the terms:
4q + 2q2 = 7q2 + 1

Reorder the terms:
4q + 2q2 = 1 + 7q2

Solving
4q + 2q2 = 1 + 7q2

Solving for variable 'q'.

Reorder the terms:
-1 + 4q + 2q2 + -7q2 = 1 + 7q2 + -1 + -7q2

Combine like terms: 2q2 + -7q2 = -5q2
-1 + 4q + -5q2 = 1 + 7q2 + -1 + -7q2

Reorder the terms:
-1 + 4q + -5q2 = 1 + -1 + 7q2 + -7q2

Combine like terms: 1 + -1 = 0
-1 + 4q + -5q2 = 0 + 7q2 + -7q2
-1 + 4q + -5q2 = 7q2 + -7q2

Combine like terms: 7q2 + -7q2 = 0
-1 + 4q + -5q2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.2 + -0.8q + q2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.8q + -0.2 + q2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.8q + q2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.8q + q2 = 0 + -0.2
-0.8q + q2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.8q + q2 = -0.2

The q term is -0.8q.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8q + 0.16 + q2 = -0.2 + 0.16

Reorder the terms:
0.16 + -0.8q + q2 = -0.2 + 0.16

Combine like terms: -0.2 + 0.16 = -0.04
0.16 + -0.8q + q2 = -0.04

Factor a perfect square on the left side:
(q + -0.4)(q + -0.4) = -0.04

Can't calculate square root of the right side.

The solution to this equation could not be determined.