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'.

Factor a trinomial.
(-6 + -1w)(13 + -2w) = 0

Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve:

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1w = 0 + 6
-1w = 0 + 6

Combine like terms: 0 + 6 = 6
-1w = 6

Divide each side by '-1'.
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(13 + -2w)' equal to zero and attempt to solve:

Simplifying
13 + -2w = 0

Solving
13 + -2w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-13' to each side of the equation.
13 + -13 + -2w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2w = 0 + -13
-2w = 0 + -13

Combine like terms: 0 + -13 = -13
-2w = -13

Divide each side by '-2'.
w = 6.5

Simplifying
w = 6.5
Solution
w = {-6, 6.5}