6w^2+19w+27=0

Solution for 6w^2+19w+27=0 equation:

Simplifying
6w2 + 19w + 27 = 0

Reorder the terms:
27 + 19w + 6w2 = 0

Solving
27 + 19w + 6w2 = 0

Solving for variable 'w'.

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

Divide each side by '6'.
4.5 + 3.166666667w + w2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 3.166666667w + -4.5 + w2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 3.166666667w + w2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 3.166666667w + w2 = 0 + -4.5
3.166666667w + w2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
3.166666667w + w2 = -4.5

The w term is 3.166666667w.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667w + 2.506944447 + w2 = -4.5 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667w + w2 = -4.5 + 2.506944447

Combine like terms: -4.5 + 2.506944447 = -1.993055553
2.506944447 + 3.166666667w + w2 = -1.993055553

Factor a perfect square on the left side:
(w + 1.583333334)(w + 1.583333334) = -1.993055553

Can't calculate square root of the right side.

The solution to this equation could not be determined.