To solve the quadratic equation \( 2x^2 + 3x - 5 = 0 \), we will use the **quadratic formula**:

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

For this equation, the coefficients are:
- \( a = 2 \)
- \( b = 3 \)
- \( c = -5 \)

Let's substitute these values into the formula:

\[
x = \frac{-3 \pm \sqrt{3^2 - 4(2)(-5)}}{2(2)}
\]

Simplifying step by step:

\[
x = \frac{-3 \pm \sqrt{9 + 40}}{4}
\]
\[
x = \frac{-3 \pm \sqrt{49}}{4}
\]
\[
x = \frac{-3 \pm 7}{4}
\]

Now, solve for the two possible values of \( x \):

1. \( x = \frac{-3 + 7}{4} = \frac{4}{4} = 1 \)
2. \( x = \frac{-3 - 7}{4} = \frac{-10}{4} = -2.5 \)

Therefore, the solutions are:
\[
x = 1 \quad \text{or} \quad x = -2.5
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you determine if a quadratic equation has real or complex solutions?
2. What are the possible methods for solving quadratic equations besides the quadratic formula?
3. How does the discriminant affect the number of solutions in a quadratic equation?
4. What is the geometric interpretation of the roots of a quadratic equation?
5. Can you derive the quadratic formula from completing the square?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the quadratic equation 2x² + 3x - 5 = 0 using the quadratic formula. This problem explores key algebraic concepts, such as quadratic equations and the discriminant, with a step-by-step solution. Ideal for students in Grades 8-10.

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