Solve the equation by any method. $$ 7 x^{2}+24 x+20=0 $$

Question

UpStudy AI · Accepted Answer

To solve the quadratic equation:

$$
7x^{2} + 24x + 20 = 0
$$

we can use the **quadratic formula**, which is given by:

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

where $$ a = 7 $$, $$ b = 24 $$, and $$ c = 20 $$.

1. **Calculate the discriminant ($$ D $$)**:

$$
D = b^2 - 4ac = 24^2 - 4 \times 7 \times 20 = 576 - 560 = 16
$$

2. **Apply the quadratic formula**:

$$
x = \frac{-24 \pm \sqrt{16}}{2 \times 7} = \frac{-24 \pm 4}{14}
$$

3. **Find the two solutions**:

- **First solution**:

$$
x = \frac{-24 + 4}{14} = \frac{-20}{14} = -\frac{10}{7}
$$

- **Second solution**:

$$
x = \frac{-24 - 4}{14} = \frac{-28}{14} = -2
$$

**Therefore, the solutions to the equation are:**

$$
x = -2 \quad \text{and} \quad x = -\frac{10}{7}
$$
The solutions are $$ x = -2 $$ and $$ x = -\frac{10}{7} $$.

Solve the equation by any method.