$$ c b x ^ { 2 } + 24 x - 30 $$

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UpStudy AI · Accepted Answer

The expression you've provided is a quadratic polynomial in terms of $$ x $$:

$$
cbx^{2} + 24x - 30
$$

To **solve for $$ x $$**, you can use the **quadratic formula**. The general form of a quadratic equation is:

$$
ax^{2} + bx + c = 0
$$

Comparing this with your equation:

- $$ a = cb $$
- $$ b = 24 $$
- $$ c = -30 $$

The quadratic formula is:

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

**Plugging in the values:**

$$
x = \frac{-24 \pm \sqrt{24^{2} - 4 \cdot cb \cdot (-30)}}{2 \cdot cb}
$$

**Simplify the discriminant ($$ \Delta $$):**

$$
\Delta = 24^{2} - 4 \cdot cb \cdot (-30) = 576 + 120cb
$$

**So, the solutions for $$ x $$ are:**

$$
x = \frac{-24 \pm \sqrt{576 + 120cb}}{2cb}
$$

**Further Simplification (Optional):**

You can factor out a common factor in the numerator and denominator if desired:

$$
x = \frac{-24 \pm \sqrt{576 + 120cb}}{2cb} = \frac{-12 \pm \frac{\sqrt{576 + 120cb}}{2}}{cb}
$$

However, the expression is already in its simplest form unless specific values for $$ c $$ and $$ b $$ are provided.

---

**Example:**

If you have specific values for $$ c $$ and $$ b $$, you can substitute them into the equation to find numerical solutions for $$ x $$. Here's how you'd do it step-by-step with hypothetical values:

1. **Assume** $$ c = 2 $$ and $$ b = 3 $$.

2. **Plug** the values into the discriminant:

$$
   \Delta = 576 + 120 \cdot 2 \cdot 3 = 576 + 720 = 1296
   $$

3. **Take** the square root of the discriminant:

$$
   \sqrt{1296} = 36
   $$

4. **Apply** the quadratic formula:

$$
   x = \frac{-24 \pm 36}{2 \cdot 2 \cdot 3} = \frac{-24 \pm 36}{12}
   $$

5. **Find** the two possible solutions:

- $$ x = \frac{-24 + 36}{12} = \frac{12}{12} = 1 $$
   - $$ x = \frac{-24 - 36}{12} = \frac{-60}{12} = -5 $$

**Solutions: $$ x = 1 $$ and $$ x = -5 $$**

*Note:* Without specific values for $$ c $$ and $$ b $$, the solutions will remain in terms of these variables.
To solve the quadratic equation $$ cbx^{2} + 24x - 30 = 0 $$, use the quadratic formula: $$ x = \frac{-24 \pm \sqrt{24^{2} - 4 \cdot cb \cdot (-30)}}{2 \cdot cb} $$ Simplify the discriminant: $$ \Delta = 576 + 120cb $$ So, the solutions are: $$ x = \frac{-24 \pm \sqrt{576 + 120cb}}{2cb} $$ If specific values for $$ c $$ and $$ b $$ are given, substitute them to find numerical solutions for $$ x $$.

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