To solve the quadratic equation \( 1x^2 - 2x - 15 = 0 \), we can use the quadratic formula:

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

For the equation \( ax^2 + bx + c = 0 \), the coefficients are:
- \( a = 1 \)
- \( b = -2 \)
- \( c = -15 \)

### Step 1: Calculate the Discriminant
The discriminant (\( \Delta \)) is given by:

\[
\Delta = b^2 - 4ac
\]

Substituting the values:

\[
\Delta = (-2)^2 - 4(1)(-15) = 4 + 60 = 64
\]

### Step 2: Apply the Quadratic Formula
Now that we have the discriminant:

\[
x = \frac{-(-2) \pm \sqrt{64}}{2(1)} = \frac{2 \pm 8}{2}
\]

This gives us two possible solutions for \( x \):

\[
x_1 = \frac{2 + 8}{2} = \frac{10}{2} = 5
\]

\[
x_2 = \frac{2 - 8}{2} = \frac{-6}{2} = -3
\]

### Solution
The solutions to the equation \( 1x^2 - 2x - 15 = 0 \) are:

\[
x = 5 \quad \text{or} \quad x = -3
\]

Would you like further details on this solution or have any questions?

### Related Questions:
1. How do you determine the nature of the roots using the discriminant?
2. What is the significance of the discriminant being positive, zero, or negative?
3. Can you graph the quadratic equation \( x^2 - 2x - 15 = 0 \) and show the points where it intersects the x-axis?
4. How can you factor the quadratic equation directly without using the quadratic formula?
5. What are the applications of quadratic equations in real-life scenarios?

### Tip:
Always check the discriminant first to understand the nature of the roots before solving a quadratic equation.

Learn how to solve the quadratic equation 1x²–2x–15=0 step by step using the quadratic formula. This problem covers essential algebraic concepts like the discriminant and quadratic equations, making it suitable for students in Grades 7-9.

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