`3x^(2)+19x=14`
If a and b are distinct solution of the equation above, what is the value of `-3ab`?

Answer

To solve the equation \(3x^2 + 19x = 14\) and find the value of \(-3ab\) where \(a\) and \(b\) are the distinct solutions of the equation, we can follow these steps:

### Step 1: Rearrange the Equation
First, we need to rearrange the equation into standard quadratic form \(ax^2 + bx + c = 0\).

\[ 3x^2 + 19x - 14 = 0 \]

### Step 2: Identify Coefficients
From the standard form, we identify the coefficients:
- \(a_1 = 3\)
- \(b_1 = 19\)
- \(c_1 = -14\)

### Step 3: Use Vieta's Formulas
According to Vieta's formulas, for a quadratic equation \(ax^2 + bx + c = 0\):
- The sum of the roots \(a + b = -\frac{b_1}{a_1}\)
- The product of the roots \(ab = \frac{c_1}{a_1}\)

In our case, we need to find \(ab\):
\[ ab = \frac{c_1}{a_1} = \frac{-14}{3} \]

### Step 4: Calculate \(-3ab\)
Now we can calculate \(-3ab\):
\[ -3ab = -3 \left(\frac{-14}{3}\right) \]

### Step 5: Simplify the Expression
Now, simplify the expression:
\[ -3ab = \frac{42}{3} = 14 \]

### Final Answer
Thus, the value of \(-3ab\) is:
\[ \boxed{14} \]

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