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The given quadratic solutions are:

\[
x = \frac{15 \pm \sqrt{-215}}{22}
\]

From the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
we can identify the corresponding values for \(a\), \(b\), and \(c\).

### Step-by-step process:

1. **Numerator comparison**:
   \[
   15 = -b \quad \text{so} \quad b = -15
   \]

2. **Denominator comparison**:
   \[
   22 = 2a \quad \text{so} \quad a = 11
   \]

3. **Discriminant comparison**:
   The discriminant is given as:
   \[
   b^2 - 4ac = -215
   \]
   Substituting \(b = -15\) and \(a = 11\):
   \[
   (-15)^2 - 4(11)(c) = -215
   \]
   Simplifying:
   \[
   225 - 44c = -215
   \]
   \[
   -44c = -215 - 225
   \]
   \[
   -44c = -440
   \]
   \[
   c = \frac{-440}{-44} = 10
   \]

### The quadratic equation:

The quadratic equation is:

\[
11x^2 - 15x + 10 = 0
\]

Would you like further details or explanations?

Here are some related questions to expand on this concept:

1. How does the discriminant determine the nature of the roots?
2. What happens if the discriminant is zero or positive?
3. Can you explain the role of the "±" sign in the quadratic formula?
4. How does factoring differ from solving using the quadratic formula?
5. How do complex numbers come into play when the discriminant is negative?

**Tip:** Always simplify the equation when using the quadratic formula to avoid common mistakes related to discriminants.

Use the Quadratic Formula to write a quadratic equation that has the solutions x = (15 ± √(-215)) / 22.

Learn how to form a quadratic equation with complex solutions from the quadratic formula. This problem covers concepts such as algebraic manipulation, discriminants, and the quadratic formula. Ideal for students in Grades 9-12.

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