The quadratic expression you've provided is \( 8x^2 - 18x + 7 \).

### To factor or solve the quadratic expression, let's go through the process step by step:

1. **Identify the coefficients**:  
   - \( a = 8 \) (coefficient of \( x^2 \))
   - \( b = -18 \) (coefficient of \( x \))
   - \( c = 7 \) (constant term)

2. **Calculate the discriminant** \( \Delta \):  
   The discriminant \( \Delta \) is given by \( \Delta = b^2 - 4ac \).  
   Substituting the values:
   \[
   \Delta = (-18)^2 - 4(8)(7) = 324 - 224 = 100
   \]

3. **Find the roots** using the quadratic formula:  
   The quadratic formula is given by:
   \[
   x = \frac{-b \pm \sqrt{\Delta}}{2a}
   \]
   Substituting the values:
   \[
   x = \frac{-(-18) \pm \sqrt{100}}{2(8)} = \frac{18 \pm 10}{16}
   \]
   Now, calculate the two possible values for \( x \):
   - \( x_1 = \frac{18 + 10}{16} = \frac{28}{16} = \frac{7}{4} \)
   - \( x_2 = \frac{18 - 10}{16} = \frac{8}{16} = \frac{1}{2} \)

So, the roots of the equation \( 8x^2 - 18x + 7 = 0 \) are \( x = \frac{7}{4} \) and \( x = \frac{1}{2} \).

### Factored form:
Using the roots, the quadratic expression can be factored as:
\[
8x^2 - 18x + 7 = 8(x - \frac{7}{4})(x - \frac{1}{2})
\]

If you have any questions or want more details, feel free to ask!

### Related Questions:
1. How do you complete the square for the quadratic equation \( 8x^2 - 18x + 7 \)?
2. What is the vertex form of the quadratic expression \( 8x^2 - 18x + 7 \)?
3. How do you graph the quadratic function \( 8x^2 - 18x + 7 \)?
4. Can the quadratic expression \( 8x^2 - 18x + 7 \) be factored by grouping?
5. What are the sum and product of the roots for the equation \( 8x^2 - 18x + 7 \)?
6. How does the discriminant help in determining the nature of roots?
7. What is the axis of symmetry for the parabola defined by \( y = 8x^2 - 18x + 7 \)?
8. How do you find the minimum or maximum value of the quadratic function \( 8x^2 - 18x + 7 \)?

### Tip:
When factoring quadratics, always check the discriminant first to determine whether the quadratic can be factored easily or if it requires the quadratic formula.

Learn how to factor and solve the quadratic equation 8x^2 - 18x + 7 with detailed step-by-step instructions. This problem covers key algebraic concepts, including the quadratic formula, discriminant, and factoring quadratics. Suitable for high school students in Grades 9-12.

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