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The given quadratic equation is:

\[
3x^2 + 20x + 25 = 0
\]

To solve this using the quadratic formula, we will apply the formula:

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

Here, the coefficients \( a \), \( b \), and \( c \) are:

- \( a = 3 \)
- \( b = 20 \)
- \( c = 25 \)

### Step 1: Calculate the discriminant
The discriminant is \( b^2 - 4ac \):

\[
\Delta = 20^2 - 4(3)(25) = 400 - 300 = 100
\]

### Step 2: Apply the quadratic formula
Now, substituting the values into the quadratic formula:

\[
x = \frac{-20 \pm \sqrt{100}}{2(3)} = \frac{-20 \pm 10}{6}
\]

This gives us two possible solutions:

\[
x_1 = \frac{-20 + 10}{6} = \frac{-10}{6} = \frac{-5}{3}
\]

\[
x_2 = \frac{-20 - 10}{6} = \frac{-30}{6} = -5
\]

### Final answer:
The solutions to the equation \( 3x^2 + 20x + 25 = 0 \) are:

\[
x_1 = \frac{-5}{3}, \quad x_2 = -5
\]

Would you like more details or have any questions on these steps?

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Here are 5 related questions:
1. How does the discriminant determine the nature of the roots of a quadratic equation?
2. What would happen if the discriminant were negative in this example?
3. Can you solve a quadratic equation by completing the square for this equation?
4. How would the quadratic formula change for a different quadratic equation, like \( x^2 - 4x + 4 = 0 \)?
5. How does the quadratic formula compare to factoring when solving quadratic equations?

**Tip:** When the discriminant (\( \Delta = b^2 - 4ac \)) is positive and a perfect square, the solutions will always be rational numbers.

Use the quadratic formula to solve. Express your answer in simplest form. 3x^2 + 20x + 25 = 0

This page explains how to solve the quadratic equation 3x^2 + 20x + 25 using the quadratic formula. Learn step-by-step how to calculate the discriminant and apply the formula to find the roots. Suitable for students in Grades 8-10.

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