https://file.aiquickdraw.com/mathbot/file/1728638763734r6gcfdpj.jpg

The equation provided in the image is:

\[
3x^2 + 5x - 3 = 0
\]

It also specifies solving this equation to two decimal places ("kahden desimaalin tarkkuudella" means "to two decimal places" in Finnish). 

### To solve the quadratic equation, we can use the quadratic formula:

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

For the equation \(3x^2 + 5x - 3 = 0\), the coefficients are:
- \(a = 3\)
- \(b = 5\)
- \(c = -3\)

Now, let's calculate the solutions:

\[
x = \frac{-5 \pm \sqrt{5^2 - 4(3)(-3)}}{2(3)}
\]
\[
x = \frac{-5 \pm \sqrt{25 + 36}}{6}
\]
\[
x = \frac{-5 \pm \sqrt{61}}{6}
\]
\[
x = \frac{-5 \pm 7.81}{6}
\]

This results in two possible solutions:
1. \(x_1 = \frac{-5 + 7.81}{6} = \frac{2.81}{6} \approx 0.47\)
2. \(x_2 = \frac{-5 - 7.81}{6} = \frac{-12.81}{6} \approx -2.14\)

### Final Solutions (to two decimal places):
- \(x_1 \approx 0.47\)
- \(x_2 \approx -2.14\)

Would you like a detailed breakdown of each step or further clarification?

Here are some related questions:
1. Can you explain how the quadratic formula works in other scenarios?
2. What happens if the discriminant (the part under the square root) is negative?
3. How do you check if the solutions to a quadratic equation are correct?
4. What are some other methods to solve quadratic equations apart from the quadratic formula?
5. How can this type of equation be applied to real-world problems?

**Tip**: Always check the discriminant (\(b^2 - 4ac\)) first to determine if the equation has real, complex, or repeated roots.

Solve the quadratic equation 3x^2 + 5x - 3 = 0 to two decimal places.

Learn how to solve the quadratic equation 3x^2 + 5x - 3 using the quadratic formula. This step-by-step solution covers algebraic concepts and calculations with answers rounded to two decimal places. Suitable for students in Grades 8-10.

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