To solve the quadratic equation \( 2x^2 + 3x - 20 = 0 \), we can again use the quadratic formula:

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

Here, \( a = 2 \), \( b = 3 \), and \( c = -20 \).

Substituting these values into the formula:

\[
x = \frac{-3 \pm \sqrt{3^2 - 4(2)(-20)}}{2(2)}
\]

Simplifying further:

\[
x = \frac{-3 \pm \sqrt{9 + 160}}{4}
\]
\[
x = \frac{-3 \pm \sqrt{169}}{4}
\]
\[
x = \frac{-3 \pm 13}{4}
\]

This gives us two possible solutions:

1. \( x_1 = \frac{-3 + 13}{4} = \frac{10}{4} = 2.5 \)
2. \( x_2 = \frac{-3 - 13}{4} = \frac{-16}{4} = -4 \)

So, the solutions are \( x = 2.5 \) and \( x = -4 \).

Would you like more details or have any questions?

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Here are some related questions you might find interesting:

1. How can you verify the solutions of a quadratic equation?
2. What is the importance of the discriminant in solving quadratic equations?
3. Can this equation be factored directly instead of using the quadratic formula?
4. How does the graph of the quadratic function \( y = 2x^2 + 3x - 20 \) look?
5. What is the vertex of the quadratic function \( y = 2x^2 + 3x - 20 \)?
6. How do you find the axis of symmetry for the function \( y = 2x^2 + 3x - 20 \)?
7. What are the roots of the quadratic function graphically?
8. Can you solve the quadratic equation by completing the square?

**Tip:** When solving a quadratic equation, make sure to simplify the square root as much as possible before proceeding to find the final roots.

Learn how to solve the quadratic equation 2x^2 + 3x - 20 = 0 with a detailed step-by-step solution. This problem involves key algebraic concepts, including the quadratic formula. Suitable for students in Grades 9-12.

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