2w^2-w+78=0

Solution for 2w^2-w+78=0 equation:

Simplifying
2w2 + -1w + 78 = 0

Reorder the terms:
78 + -1w + 2w2 = 0

Solving
78 + -1w + 2w2 = 0

Solving for variable 'w'.

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

Divide each side by '2'.
39 + -0.5w + w2 = 0

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + -0.5w + -39 + w2 = 0 + -39

Reorder the terms:
39 + -39 + -0.5w + w2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -0.5w + w2 = 0 + -39
-0.5w + w2 = 0 + -39

Combine like terms: 0 + -39 = -39
-0.5w + w2 = -39

The w term is -0.5w.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5w + 0.0625 + w2 = -39 + 0.0625

Reorder the terms:
0.0625 + -0.5w + w2 = -39 + 0.0625

Combine like terms: -39 + 0.0625 = -38.9375
0.0625 + -0.5w + w2 = -38.9375

Factor a perfect square on the left side:
(w + -0.25)(w + -0.25) = -38.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.