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

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

where:
- \( a = 2 \)
- \( b = 5 \)
- \( c = -3 \)

### Step 1: Identify the coefficients
- \( a = 2 \)
- \( b = 5 \)
- \( c = -3 \)

### Step 2: Substitute the values into the quadratic formula

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

\[
x = \frac{-5 \pm \sqrt{25 + 24}}{4}
\]

\[
x = \frac{-5 \pm \sqrt{49}}{4}
\]

### Step 3: Simplify

\[
x = \frac{-5 \pm 7}{4}
\]

### Step 4: Find the two solutions

1. **First solution**:
   \[
   x = \frac{-5 + 7}{4} = \frac{2}{4} = \frac{1}{2}
   \]

2. **Second solution**:
   \[
   x = \frac{-5 - 7}{4} = \frac{-12}{4} = -3
   \]

### Final Answer:
\[
x = \frac{1}{2} \text{ or } x = -3
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How do you derive the quadratic formula?
2. What are other methods to solve quadratic equations?
3. How can you determine the nature of the roots using the discriminant?
4. What is the significance of the coefficients \( a \), \( b \), and \( c \) in a quadratic equation?
5. Can you graph the quadratic equation and find the solutions visually?

**Tip:** Always check the discriminant \( b^2 - 4ac \) before solving. If it's positive, you get two real solutions; if zero, one real solution; and if negative, two complex solutions.

Explore a step-by-step solution to solve the quadratic equation 2x^2 + 5x - 3 = 0 using the quadratic formula. This solution provides insight into key algebraic concepts, including finding roots of equations. Perfect for students in Grades 8-10.

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