Check whether the equation given below is a quadratic equation
`x(x+1) +8=(x+2)(x-2)`

Answer

To determine whether the equation \( x(x+1) + 8 = (x+2)(x-2) \) is a quadratic equation, we will simplify both sides and check the highest power of \( x \).

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ x(x+1) + 8 = (x+2)(x-2) \]

2. **Expand both sides of the equation:**
- Left side:
\[ x(x+1) + 8 = x^2 + x + 8 \]
- Right side:
\[ (x+2)(x-2) = x^2 - 2^2 = x^2 - 4 \]

3. **Set the expanded forms equal to each other:**
\[ x^2 + x + 8 = x^2 - 4 \]

4. **Subtract \( x^2 \) from both sides:**
\[ x + 8 = -4 \]

5. **Rearrange the equation to isolate \( x \):**
\[ x + 8 + 4 = 0 \quad \Rightarrow \quad x + 12 = 0 \]

6. **Solve for \( x \):**
\[ x = -12 \]

7. **Identify the highest power of \( x \):**
The highest power of \( x \) in the equation is \( 1 \) (from \( x + 12 = 0 \)), which indicates that the equation is linear, not quadratic.

### Conclusion:
Since the highest power of \( x \) is \( 1 \), the given equation is not a quadratic equation.