4x^2+x+6=0

Solution for 4x^2+x+6=0 equation:

Simplifying
4x2 + x + 6 = 0

Reorder the terms:
6 + x + 4x2 = 0

Solving
6 + x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
1.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.25x + x2 = 0 + -1.5
0.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.25x + x2 = -1.5

The x term is x.  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.
0.25x + 0.25 + x2 = -1.5 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + 0.25x + x2 = -1.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.