4w^2+5w+6=0

Solution for 4w^2+5w+6=0 equation:

Simplifying
4w2 + 5w + 6 = 0

Reorder the terms:
6 + 5w + 4w2 = 0

Solving
6 + 5w + 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 + 1.25w + w2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 1.25w + -1.5 + w2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 1.25w + w2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 1.25w + w2 = 0 + -1.5
1.25w + w2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
1.25w + w2 = -1.5

The w term is 1.25w.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25w + 0.390625 + w2 = -1.5 + 0.390625

Reorder the terms:
0.390625 + 1.25w + w2 = -1.5 + 0.390625

Combine like terms: -1.5 + 0.390625 = -1.109375
0.390625 + 1.25w + w2 = -1.109375

Factor a perfect square on the left side:
(w + 0.625)(w + 0.625) = -1.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.