5k^2+k+3=0

Solution for 5k^2+k+3=0 equation:

Simplifying
5k2 + k + 3 = 0

Reorder the terms:
3 + k + 5k2 = 0

Solving
3 + k + 5k2 = 0

Solving for variable 'k'.

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

Divide each side by '5'.
0.6 + 0.2k + k2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 0.2k + -0.6 + k2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 0.2k + k2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 0.2k + k2 = 0 + -0.6
0.2k + k2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
0.2k + k2 = -0.6

The k term is k.  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.
0.2k + 0.25 + k2 = -0.6 + 0.25

Reorder the terms:
0.25 + 0.2k + k2 = -0.6 + 0.25

Combine like terms: -0.6 + 0.25 = -0.35
0.25 + 0.2k + k2 = -0.35

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = -0.35

Can't calculate square root of the right side.

The solution to this equation could not be determined.