Solve

1/w=7/w-1/3

I came up with 18 for the solution

I got the same solution.

Thank you!

To solve the equation 1/w = 7/(w - 1/3), we can follow these steps:

Step 1: Simplify the equation by finding a common denominator.
- The denominator of the left side is w, while the denominator of the right side is (w - 1/3).
- To find a common denominator, we need to multiply the left side by (w - 1/3) and the right side by w.

Step 2: Apply the distributive property and simplify.
- The equation becomes (w - 1/3) * 1/w = 7w.
- Simplifying further, we have (w - 1/3)/w = 7w.

Step 3: Solve for w by cross multiplying.
- Cross-multiplying, we get (w - 1/3) = 7w * w.
- Expanding the right side, we have (w - 1/3) = 7w^2.

Step 4: Rearrange the equation and bring all terms to one side.
- Rewrite the equation in standard form: 7w^2 - w + 1/3 = 0.
- Multiply the entire equation by 3 to get rid of the fraction: 21w^2 - 3w + 1 = 0.

Step 5: Solve the quadratic equation.
- We can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula x = (-b ± √(b^2 - 4ac))/(2a).
- Applying this formula to our equation, we have w = (-(-3) ± √((-3)^2 - 4*21*1))/(2*21).
- Simplifying, we get w = (3 ± √(9 - 84))/42.
- Further simplifying, we have w = (3 ± √(-75))/42.

Step 6: Determine the nature of the solutions.
- The term inside the square root, -75, is negative. This indicates that the equation has no real solutions since the square root of a negative number is not a real number.

Therefore, the equation 1/w = 7/(w - 1/3) has no real solutions.