https://file.aiquickdraw.com/mathbot/file/17270302788775btprzvt.jpg

The equation shown in the image is:

\[
3x^2 - 2x = 3
\]

To solve this using the quadratic formula, we first need to rewrite the equation in standard quadratic form:

\[
3x^2 - 2x - 3 = 0
\]

The quadratic formula is given by:

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

For the equation \(3x^2 - 2x - 3 = 0\), the coefficients are:
- \(a = 3\)
- \(b = -2\)
- \(c = -3\)

Now we can substitute these values into the quadratic formula:

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

I'll calculate this step by step.The solutions to the quadratic equation \(3x^2 - 2x - 3 = 0\) are:

\[
x_1 = 1.39 \quad \text{and} \quad x_2 = -0.72
\]

Both are rounded to the nearest hundredth.

Would you like more details or have any other questions? Here are 5 related questions for practice:

1. How can you verify the solutions of a quadratic equation?
2. What happens if the discriminant in the quadratic formula is negative?
3. How do you determine the vertex of a quadratic function?
4. Can a quadratic equation have only one solution? Under what conditions?
5. How can you factorize a quadratic equation instead of using the quadratic formula?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) before using the quadratic formula, as it tells you how many real solutions the equation has.

Use the quadratic formula to solve for x in the equation 3x^2 - 2x = 3. Round your answer to the nearest hundredth.

Learn how to solve the quadratic equation 3x^2 - 2x = 3 using the quadratic formula. This step-by-step guide covers key algebraic concepts and explains how to apply the quadratic formula. Solutions are rounded to the nearest hundredth, suitable for students in Grades 9-10.

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