5n^2+n=-6

Solution for 5n^2+n=-6 equation:

Simplifying
5n2 + n = -6

Reorder the terms:
n + 5n2 = -6

Solving
n + 5n2 = -6

Solving for variable 'n'.

Reorder the terms:
6 + n + 5n2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + n + 5n2 = 0

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

Divide each side by '5'.
1.2 + 0.2n + n2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 0.2n + -1.2 + n2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 0.2n + n2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 0.2n + n2 = 0 + -1.2
0.2n + n2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
0.2n + n2 = -1.2

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.
0.2n + 0.25 + n2 = -1.2 + 0.25

Reorder the terms:
0.25 + 0.2n + n2 = -1.2 + 0.25

Combine like terms: -1.2 + 0.25 = -0.95
0.25 + 0.2n + n2 = -0.95

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.95

Can't calculate square root of the right side.

The solution to this equation could not be determined.