2n^2+n+6=0

Solution for 2n^2+n+6=0 equation:

Simplifying
2n2 + n + 6 = 0

Reorder the terms:
6 + n + 2n2 = 0

Solving
6 + n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
3 + 0.5n + n2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 0.5n + -3 + n2 = 0 + -3

Reorder the terms:
3 + -3 + 0.5n + n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 0.5n + n2 = 0 + -3
0.5n + n2 = 0 + -3

Combine like terms: 0 + -3 = -3
0.5n + n2 = -3

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5n + 0.25 + n2 = -3 + 0.25

Reorder the terms:
0.25 + 0.5n + n2 = -3 + 0.25

Combine like terms: -3 + 0.25 = -2.75
0.25 + 0.5n + n2 = -2.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.