5n^2-n+6=0

Solution for 5n^2-n+6=0 equation:

Simplifying
5n2 + -1n + 6 = 0

Reorder the terms:
6 + -1n + 5n2 = 0

Solving
6 + -1n + 5n2 = 0

Solving for variable 'n'.

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 -0.2n.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2n + 0.01 + n2 = -1.2 + 0.01

Reorder the terms:
0.01 + -0.2n + n2 = -1.2 + 0.01

Combine like terms: -1.2 + 0.01 = -1.19
0.01 + -0.2n + n2 = -1.19

Factor a perfect square on the left side:
(n + -0.1)(n + -0.1) = -1.19

Can't calculate square root of the right side.

The solution to this equation could not be determined.