The given equation is a quadratic equation:

\[
x^2 + 3x - 2 = 0
\]

To solve this quadratic equation, we can use the quadratic formula:

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

where \(a\), \(b\), and \(c\) are the coefficients from the equation \(ax^2 + bx + c = 0\). For this equation:

- \(a = 1\)
- \(b = 3\)
- \(c = -2\)

Substituting these values into the formula:

\[
x = \frac{{-3 \pm \sqrt{{3^2 - 4 \cdot 1 \cdot (-2)}}}}{2 \cdot 1}
\]

Simplify under the square root:

\[
x = \frac{{-3 \pm \sqrt{{9 + 8}}}}{2}
\]

\[
x = \frac{{-3 \pm \sqrt{17}}}{2}
\]

So, the solutions for \(x\) are:

\[
x = \frac{{-3 + \sqrt{17}}}{2} \quad \text{and} \quad x = \frac{{-3 - \sqrt{17}}}{2}
\]

Would you like further details or have any questions?

Here are some related questions to explore:

1. How do you complete the square to solve a quadratic equation?
2. Can a quadratic equation have complex solutions?
3. How do you factor a quadratic equation when it's factorable?
4. What are the properties of the discriminant in a quadratic equation?
5. How can you graph a quadratic function, and what does its graph represent?

**Tip:** The discriminant (\(b^2 - 4ac\)) determines the nature of the roots: if it's positive, the equation has two real roots; if zero, one real root; and if negative, two complex roots.

Explore how to solve the quadratic equation x² + 3x - 2 = 0 step by step using the quadratic formula. This guide covers essential algebraic concepts and is ideal for students in Grades 9-10.

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