https://file.aiquickdraw.com/mathbot/file/1726457189570plon7f8t.jpg

The equation provided in the image is:

\[
x(3x - 1) = 10
\]

### Step-by-step solution:

1. **Expand the equation** by distributing \(x\) to both terms inside the parentheses:
   \[
   x(3x - 1) = 10 \quad \Rightarrow \quad 3x^2 - x = 10
   \]

2. **Rearrange the equation** to set it to zero:
   \[
   3x^2 - x - 10 = 0
   \]

3. **Solve the quadratic equation** using the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   For the equation \(3x^2 - x - 10 = 0\), the coefficients are:
   \[
   a = 3, \quad b = -1, \quad c = -10
   \]

4. **Substitute the values into the quadratic formula**:
   \[
   x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(-10)}}{2(3)}
   \]
   Simplifying:
   \[
   x = \frac{1 \pm \sqrt{1 + 120}}{6} \quad \Rightarrow \quad x = \frac{1 \pm \sqrt{121}}{6}
   \]
   \[
   x = \frac{1 \pm 11}{6}
   \]

5. **Find the two possible solutions**:
   \[
   x = \frac{1 + 11}{6} = \frac{12}{6} = 2
   \]
   \[
   x = \frac{1 - 11}{6} = \frac{-10}{6} = \frac{-5}{3}
   \]

### Final solutions:
The two solutions are:
\[
x = 2 \quad \text{or} \quad x = \frac{-5}{3}
\]

Would you like more details on any step, or do you have any questions?

### Related Questions:
1. What is the quadratic formula and how is it derived?
2. How can you check if your solutions are correct for quadratic equations?
3. What happens if the discriminant (inside the square root) is negative?
4. How can we solve quadratic equations by factoring instead of using the quadratic formula?
5. What are the different methods for solving quadratic equations?

### Tip:
Always verify your solutions by plugging them back into the original equation to see if they satisfy it.

Learn how to solve the quadratic equation x(3x - 1) = 10 with a step-by-step solution. This algebra problem covers key concepts such as expanding expressions and solving quadratic equations using the quadratic formula. Suitable for students in Grades 8-10.

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