5n^2+3n+1=0

Solution for 5n^2+3n+1=0 equation:

Simplifying
5n2 + 3n + 1 = 0

Reorder the terms:
1 + 3n + 5n2 = 0

Solving
1 + 3n + 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'.
0.2 + 0.6n + n2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 0.6n + -0.2 + n2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 0.6n + n2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 0.6n + n2 = 0 + -0.2
0.6n + n2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
0.6n + n2 = -0.2

The n term is 0.6n.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6n + 0.09 + n2 = -0.2 + 0.09

Reorder the terms:
0.09 + 0.6n + n2 = -0.2 + 0.09

Combine like terms: -0.2 + 0.09 = -0.11
0.09 + 0.6n + n2 = -0.11

Factor a perfect square on the left side:
(n + 0.3)(n + 0.3) = -0.11

Can't calculate square root of the right side.

The solution to this equation could not be determined.