To solve the quadratic equation \( 5x^2 + 70x + 240 = 0 \), we can use the quadratic formula:

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

Here, \( a = 5 \), \( b = 70 \), and \( c = 240 \).

### Step 1: Calculate the discriminant
\[
\text{Discriminant} = b^2 - 4ac = 70^2 - 4(5)(240)
\]
\[
\text{Discriminant} = 4900 - 4800 = 100
\]

### Step 2: Apply the quadratic formula
\[
x = \frac{-70 \pm \sqrt{100}}{2(5)}
\]
\[
x = \frac{-70 \pm 10}{10}
\]

### Step 3: Solve for the roots
\[
x_1 = \frac{-70 + 10}{10} = \frac{-60}{10} = -6
\]
\[
x_2 = \frac{-70 - 10}{10} = \frac{-80}{10} = -8
\]

### Final Answer
The solutions are \( x = -6 \) and \( x = -8 \).

Would you like further details or have any other questions?

Here are five related questions:
1. What is the vertex of the parabola \( 5x^2 + 70x + 240 \)?
2. How can you factor the quadratic equation \( 5x^2 + 70x + 240 = 0 \)?
3. What is the axis of symmetry for the equation \( 5x^2 + 70x + 240 = 0 \)?
4. How does the discriminant determine the nature of the roots?
5. How would the graph of \( 5x^2 + 70x + 240 = 0 \) look?

**Tip:** Always check the discriminant to determine whether the roots are real or complex before solving the quadratic equation.

Learn how to solve the quadratic equation 5x^2 + 70x + 240 = 0 with a detailed step-by-step solution. This problem involves using the quadratic formula and calculating the discriminant. Suitable for high school students (Grades 10-12) studying algebra.

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