4w^2=5w-1

Solution for 4w^2=5w-1 equation:

Simplifying
4w2 = 5w + -1

Reorder the terms:
4w2 = -1 + 5w

Solving
4w2 = -1 + 5w

Solving for variable 'w'.

Reorder the terms:
1 + -5w + 4w2 = -1 + 5w + 1 + -5w

Reorder the terms:
1 + -5w + 4w2 = -1 + 1 + 5w + -5w

Combine like terms: -1 + 1 = 0
1 + -5w + 4w2 = 0 + 5w + -5w
1 + -5w + 4w2 = 5w + -5w

Combine like terms: 5w + -5w = 0
1 + -5w + 4w2 = 0

Factor a trinomial.
(1 + -4w)(1 + -1w) = 0

Subproblem 1
Set the factor '(1 + -4w)' equal to zero and attempt to solve:

Simplifying
1 + -4w = 0

Solving
1 + -4w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4w = 0 + -1
-4w = 0 + -1

Combine like terms: 0 + -1 = -1
-4w = -1

Divide each side by '-4'.
w = 0.25

Simplifying
w = 0.25
Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Solution
w = {0.25, 1}