To solve the quadratic equation \(2x^2 - 17x + 21 = 0\), we can use the quadratic formula:

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

where \(a = 2\), \(b = -17\), and \(c = 21\). Let's substitute these values into the formula.

1. **Calculate the discriminant**:

\[
b^2 - 4ac = (-17)^2 - 4 \cdot 2 \cdot 21
\]

\[
b^2 - 4ac = 289 - 168 = 121
\]

2. **Compute the square root of the discriminant**:

\[
\sqrt{121} = 11
\]

3. **Apply the quadratic formula**:

\[
x = \frac{-(-17) \pm 11}{2 \cdot 2}
\]

\[
x = \frac{17 \pm 11}{4}
\]

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

- \(x_1 = \frac{17 + 11}{4} = \frac{28}{4} = 7\)
- \(x_2 = \frac{17 - 11}{4} = \frac{6}{4} = 1.5\)

So, the solutions to the quadratic equation \(2x^2 - 17x + 21 = 0\) are:

\[
\boxed{x = 7 \text{ and } x = 1.5}
\]

### Would you like more details or have any questions?

### Related Questions:
1. How do you complete the square for the equation \(2x^2 - 17x + 21 = 0\)?
2. What is the axis of symmetry for the parabola represented by \(2x^2 - 17x + 21\)?
3. How do you determine the vertex of the parabola given by \(2x^2 - 17x + 21\)?
4. Can we factor the quadratic equation \(2x^2 - 17x + 21 = 0\) instead of using the quadratic formula?
5. What is the sum and product of the roots of the equation \(2x^2 - 17x + 21 = 0\)?

### Tip:
Always check if a quadratic equation can be factored easily before using the quadratic formula; sometimes it saves time!

Learn how to solve the quadratic equation 2x^2 - 17x + 21 with a step-by-step solution using the quadratic formula. Calculate the discriminant and find the roots of the equation. Suitable for high school students.

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