114=4w^2-5w

Solution for 114=4w^2-5w equation:

Simplifying
114 = 4w2 + -5w

Reorder the terms:
114 = -5w + 4w2

Solving
114 = -5w + 4w2

Solving for variable 'w'.

Reorder the terms:
114 + 5w + -4w2 = -5w + 5w + 4w2 + -4w2

Combine like terms: -5w + 5w = 0
114 + 5w + -4w2 = 0 + 4w2 + -4w2
114 + 5w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
114 + 5w + -4w2 = 0

Factor a trinomial.
(6 + -1w)(19 + 4w) = 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 '(19 + 4w)' equal to zero and attempt to solve:

Simplifying
19 + 4w = 0

Solving
19 + 4w = 0

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

Add '-19' to each side of the equation.
19 + -19 + 4w = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 4w = 0 + -19
4w = 0 + -19

Combine like terms: 0 + -19 = -19
4w = -19

Divide each side by '4'.
w = -4.75

Simplifying
w = -4.75
Solution
w = {6, -4.75}