4w^2+9w+6=0

Solution for 4w^2+9w+6=0 equation:

Simplifying
4w2 + 9w + 6 = 0

Reorder the terms:
6 + 9w + 4w2 = 0

Solving
6 + 9w + 4w2 = 0

Solving for variable 'w'.

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

Divide each side by '4'.
1.5 + 2.25w + w2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 2.25w + -1.5 + w2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 2.25w + w2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 2.25w + w2 = 0 + -1.5
2.25w + w2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
2.25w + w2 = -1.5

The w term is 2.25w.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25w + 1.265625 + w2 = -1.5 + 1.265625

Reorder the terms:
1.265625 + 2.25w + w2 = -1.5 + 1.265625

Combine like terms: -1.5 + 1.265625 = -0.234375
1.265625 + 2.25w + w2 = -0.234375

Factor a perfect square on the left side:
(w + 1.125)(w + 1.125) = -0.234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.