2w^2=7w+4

Solution for 2w^2=7w+4 equation:

Simplifying
2w2 = 7w + 4

Reorder the terms:
2w2 = 4 + 7w

Solving
2w2 = 4 + 7w

Solving for variable 'w'.

Reorder the terms:
-4 + -7w + 2w2 = 4 + 7w + -4 + -7w

Reorder the terms:
-4 + -7w + 2w2 = 4 + -4 + 7w + -7w

Combine like terms: 4 + -4 = 0
-4 + -7w + 2w2 = 0 + 7w + -7w
-4 + -7w + 2w2 = 7w + -7w

Combine like terms: 7w + -7w = 0
-4 + -7w + 2w2 = 0

Factor a trinomial.
(-1 + -2w)(4 + -1w) = 0

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

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 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 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
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 = {-0.5, 4}