https://file.aiquickdraw.com/mathbot/file/1724237195179i2ugx9k8.jpg

From the clearer image you've provided, it appears there are algebraic expressions and a fraction. Here’s what I can interpret:

1. **Expression on the left side:**
   \[
   2x^2 - 2xy - 2 = 0
   \]

2. **Expressions on the right side:**
   \[
   \frac{49}{5} = \frac{49}{100a}
   \]

I'll solve both parts separately.

### Part 1: Solving the Algebraic Expression

Given:
\[
2x^2 - 2xy - 2 = 0
\]

We can simplify by dividing the entire equation by 2:
\[
x^2 - xy - 1 = 0
\]

This is a quadratic equation in terms of \(x\). To solve for \(x\), we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Here, \(a = 1\), \(b = -y\), and \(c = -1\).

Substituting these values:
\[
x = \frac{-(-y) \pm \sqrt{(-y)^2 - 4(1)(-1)}}{2(1)}
\]
\[
x = \frac{y \pm \sqrt{y^2 + 4}}{2}
\]

So, the solutions for \(x\) are:
\[
x = \frac{y + \sqrt{y^2 + 4}}{2} \quad \text{or} \quad x = \frac{y - \sqrt{y^2 + 4}}{2}
\]

### Part 2: Solving the Fractional Equation

Given:
\[
\frac{49}{5} = \frac{49}{100a}
\]

To solve for \(a\), cross-multiply:
\[
49 \times 100a = 49 \times 5
\]

This simplifies to:
\[
100a = 5
\]

Solving for \(a\):
\[
a = \frac{5}{100} = \frac{1}{20}
\]

### Summary of Solutions:

1. **For the quadratic equation:**
   \[
   x = \frac{y + \sqrt{y^2 + 4}}{2} \quad \text{or} \quad x = \frac{y - \sqrt{y^2 + 4}}{2}
   \]
2. **For the fractional equation:**
   \[
   a = \frac{1}{20}
   \]

Would you like more details or have any further questions?

### Relative Questions:
1. How do you use the quadratic formula for solving other quadratic equations?
2. What are the methods for solving equations involving fractions?
3. Can the quadratic equation be factored instead of using the quadratic formula?
4. How can you determine the nature of the roots using the discriminant?
5. How would you solve a quadratic equation if it had complex roots?

### Tip:
Always simplify the equation as much as possible before solving. It makes calculations easier and reduces the chance of errors.

Learn how to solve complex algebraic and fractional equations step-by-step with detailed explanations. This problem covers key concepts such as quadratic equations, fractions in equations, and algebraic expressions.

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