5w^2-4=19w

Solution for 5w^2-4=19w equation:

Simplifying
5w2 + -4 = 19w

Reorder the terms:
-4 + 5w2 = 19w

Solving
-4 + 5w2 = 19w

Solving for variable 'w'.

Reorder the terms:
-4 + -19w + 5w2 = 19w + -19w

Combine like terms: 19w + -19w = 0
-4 + -19w + 5w2 = 0

Factor a trinomial.
(-1 + -5w)(4 + -1w) = 0

Subproblem 1
Set the factor '(-1 + -5w)' equal to zero and attempt to solve:

Simplifying
-1 + -5w = 0

Solving
-1 + -5w = 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 + -5w = 0 + 1

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

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

Divide each side by '-5'.
w = -0.2

Simplifying
w = -0.2
Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

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

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

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

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-0.2, 4}