To solve the quadratic equation \(2x^2 - 7x + 3 = 0\), we can use the quadratic formula:

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

Here, \(a = 2\), \(b = -7\), and \(c = 3\). Plugging these values into the quadratic formula, we get:

\[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 2 \cdot 3}}{2 \cdot 2} \]
\[ x = \frac{7 \pm \sqrt{49 - 24}}{4} \]
\[ x = \frac{7 \pm \sqrt{25}}{4} \]
\[ x = \frac{7 \pm 5}{4} \]

This gives us two solutions:

\[ x = \frac{7 + 5}{4} = \frac{12}{4} = 3 \]
\[ x = \frac{7 - 5}{4} = \frac{2}{4} = \frac{1}{2} \]

Therefore, the solutions to the quadratic equation \(2x^2 - 7x + 3 = 0\) are \(x = 3\) and \(x = \frac{1}{2}\).

Would you like more details or have any questions?

Here are 8 relative questions to expand your understanding:

1. How do you factor a quadratic equation if it can be factored?
2. What is the discriminant, and how does it determine the nature of the roots of a quadratic equation?
3. Can you solve a quadratic equation using the method of completing the square?
4. How do you graph a quadratic function and identify its vertex?
5. What is the importance of the axis of symmetry in a quadratic function?
6. How do you find the maximum or minimum value of a quadratic function?
7. How can quadratic equations be applied in physics and engineering problems?
8. What are the properties of the roots of a quadratic equation when the discriminant is zero or negative?

**Tip:** Always check if the quadratic equation can be factored easily before using the quadratic formula, as factoring can sometimes provide a quicker solution.

Learn how to solve the quadratic equation 2x² - 7x + 3 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula and its application. Suitable for high school students.

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