https://file.aiquickdraw.com/mathbot/file/17284993950826f0fd2pt.jpg

The equation shown in the image is:

\[
\frac{x}{7} - \frac{18}{7x} = -1
\]

To solve this equation, let's follow these steps:

### Step 1: Eliminate the fractions
Multiply the entire equation by \(7x\) to get rid of the denominators.

\[
7x \cdot \left( \frac{x}{7} - \frac{18}{7x} \right) = 7x \cdot (-1)
\]

Simplifying:

\[
x^2 - 18 = -7x
\]

### Step 2: Rearrange the equation
Bring all terms to one side of the equation:

\[
x^2 + 7x - 18 = 0
\]

Now we have a quadratic equation.

### Step 3: Solve the quadratic equation
Use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \(x^2 + 7x - 18 = 0\), the coefficients are \(a = 1\), \(b = 7\), and \(c = -18\).

Substituting these values into the quadratic formula:

\[
x = \frac{-7 \pm \sqrt{7^2 - 4(1)(-18)}}{2(1)}
\]
\[
x = \frac{-7 \pm \sqrt{49 + 72}}{2}
\]
\[
x = \frac{-7 \pm \sqrt{121}}{2}
\]
\[
x = \frac{-7 \pm 11}{2}
\]

### Step 4: Calculate the two possible solutions

1. \(x = \frac{-7 + 11}{2} = \frac{4}{2} = 2\)
2. \(x = \frac{-7 - 11}{2} = \frac{-18}{2} = -9\)

### Final Answer:
The two possible solutions are:
\[
x = 2 \quad \text{or} \quad x = -9
\]

Do you need any further details or have questions about the solution process?

### Here are some related questions to explore:

1. How do you factor quadratic equations instead of using the quadratic formula?
2. What are the different methods for solving quadratic equations?
3. Can the discriminant in the quadratic formula tell us anything about the type of solutions?
4. How do we handle quadratic equations when the coefficient of \(x^2\) is not 1?
5. How do you complete the square to solve quadratic equations?

#### Tip: 
When solving quadratic equations, always check if the quadratic can be factored easily before using the quadratic formula—it can save time!

Solve the following equation: x/7 - 18/(7x) = -1

Learn how to solve the quadratic equation x/7 - 18/(7x) = -1 with a detailed step-by-step solution. This problem covers algebraic concepts and uses the quadratic formula. Suitable for students in Grades 9-11.

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