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### Extracted Content:

The image appears to contain two exercises:

**Exercise 1:**  
Calculate the value of the following expressions, assuming all variables are non-negative:
1. \( A = \frac{\sqrt{3}}{\sqrt{12}} \)
2. \( B = \frac{8}{4 \times \frac{1}{2}} \)
3. \( C = \frac{3}{2} - \frac{7}{2} \)

**Exercise 2:**  
Solve the following quadratic equation:  
\[ ax^2 + bx + c = 0 \]  
For the equation \( 2x^2 - 10x - 50 = 0 \).

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### Solutions:

**Exercise 1:**

1. **\( A = \frac{\sqrt{3}}{\sqrt{12}} \)**

   Simplify the expression:
   \[
   A = \frac{\sqrt{3}}{\sqrt{12}} = \frac{\sqrt{3}}{\sqrt{4 \times 3}} = \frac{\sqrt{3}}{2\sqrt{3}} = \frac{1}{2}
   \]
   So, \( A = \frac{1}{2} \).

2. **\( B = \frac{8}{4 \times \frac{1}{2}} \)**

   Simplify the expression:
   \[
   B = \frac{8}{4 \times \frac{1}{2}} = \frac{8}{2} = 4
   \]
   So, \( B = 4 \).

3. **\( C = \frac{3}{2} - \frac{7}{2} \)**

   Combine the fractions:
   \[
   C = \frac{3}{2} - \frac{7}{2} = \frac{3 - 7}{2} = \frac{-4}{2} = -2
   \]
   So, \( C = -2 \).

---

**Exercise 2:**

Solve the quadratic equation \( 2x^2 - 10x - 50 = 0 \).

To solve the quadratic equation, we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For the given equation \( 2x^2 - 10x - 50 = 0 \), the coefficients are:
- \( a = 2 \)
- \( b = -10 \)
- \( c = -50 \)

Now, apply the quadratic formula:
\[
x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4(2)(-50)}}{2(2)}
\]
\[
x = \frac{10 \pm \sqrt{100 + 400}}{4}
\]
\[
x = \frac{10 \pm \sqrt{500}}{4} = \frac{10 \pm 10\sqrt{5}}{4}
\]
\[
x = \frac{10(1 \pm \sqrt{5})}{4} = \frac{5(1 \pm \sqrt{5})}{2}
\]
So, the solutions are:
\[
x = \frac{5(1 + \sqrt{5})}{2} \quad \text{or} \quad x = \frac{5(1 - \sqrt{5})}{2}
\]

---

Would you like any further details or have any questions? 

### Related Questions:
1. How can we simplify expressions involving square roots in general?
2. What are the steps to solve any quadratic equation using the quadratic formula?
3. How does the discriminant in the quadratic formula help in understanding the nature of the roots?
4. Can we solve quadratic equations by factoring instead of using the quadratic formula?
5. What is the significance of the coefficients in a quadratic equation?

### Tip:
When simplifying square roots, remember to factor the number under the root into its prime factors to make it easier to simplify.

Calculate or solve the following mathematical expressions and equation.

Learn how to simplify algebraic expressions like \( \frac{\sqrt{3}}{\sqrt{12}} \) and solve quadratic equations like \( 2x^2 - 10x - 50 = 0 \). This guide covers key algebraic concepts suitable for students in Grades 8-10.

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