7w^2-4w-3=0

Solution for 7w^2-4w-3=0 equation:

Simplifying
7w2 + -4w + -3 = 0

Reorder the terms:
-3 + -4w + 7w2 = 0

Solving
-3 + -4w + 7w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -7w)(1 + -1w) = 0

Subproblem 1
Set the factor '(-3 + -7w)' equal to zero and attempt to solve:

Simplifying
-3 + -7w = 0

Solving
-3 + -7w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7w = 0 + 3
-7w = 0 + 3

Combine like terms: 0 + 3 = 3
-7w = 3

Divide each side by '-7'.
w = -0.4285714286

Simplifying
w = -0.4285714286
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 = {-0.4285714286, 1}