2r^2+r+6=0

Solution for 2r^2+r+6=0 equation:

Simplifying
2r2 + r + 6 = 0

Reorder the terms:
6 + r + 2r2 = 0

Solving
6 + r + 2r2 = 0

Solving for variable 'r'.

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

Divide each side by '2'.
3 + 0.5r + r2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 0.5r + -3 + r2 = 0 + -3

Reorder the terms:
3 + -3 + 0.5r + r2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 0.5r + r2 = 0 + -3
0.5r + r2 = 0 + -3

Combine like terms: 0 + -3 = -3
0.5r + r2 = -3

The r term is r.  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.
0.5r + 0.25 + r2 = -3 + 0.25

Reorder the terms:
0.25 + 0.5r + r2 = -3 + 0.25

Combine like terms: -3 + 0.25 = -2.75
0.25 + 0.5r + r2 = -2.75

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.