5n^2+8=-n

Solution for 5n^2+8=-n equation:

Simplifying
5n2 + 8 = -1n

Reorder the terms:
8 + 5n2 = -1n

Solving
8 + 5n2 = -1n

Solving for variable 'n'.

Reorder the terms:
8 + n + 5n2 = -1n + n

Combine like terms: -1n + n = 0
8 + n + 5n2 = 0

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

Divide each side by '5'.
1.6 + 0.2n + n2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + 0.2n + -1.6 + n2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + 0.2n + n2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 0.2n + n2 = 0 + -1.6
0.2n + n2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
0.2n + n2 = -1.6

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 = -1.6 + 0.25

Reorder the terms:
0.25 + 0.2n + n2 = -1.6 + 0.25

Combine like terms: -1.6 + 0.25 = -1.35
0.25 + 0.2n + n2 = -1.35

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -1.35

Can't calculate square root of the right side.

The solution to this equation could not be determined.