If `x=1(1)/(2)` is a solution of the equation `2x^(2)+px-6=0`, find the value of 'p'.

Answer

To find the value of \( p \) in the quadratic equation \( 2x^2 + px - 6 = 0 \) given that \( x = 1 \frac{1}{2} \) (which is equivalent to \( \frac{3}{2} \)) is a solution, we can follow these steps:

### Step 1: Substitute the value of \( x \)
Since \( x = \frac{3}{2} \) is a solution of the equation, we can substitute \( x \) into the equation:

\[ 2\left(\frac{3}{2}\right)^2 + p\left(\frac{3}{2}\right) - 6 = 0 \]

### Step 2: Calculate \( \left(\frac{3}{2}\right)^2 \)
Calculating \( \left(\frac{3}{2}\right)^2 \):

\[ \left(\frac{3}{2}\right)^2 = \frac{9}{4} \]

### Step 3: Substitute back into the equation
Now substituting this back into the equation gives:

\[ 2 \cdot \frac{9}{4} + p \cdot \frac{3}{2} - 6 = 0 \]

### Step 4: Simplify \( 2 \cdot \frac{9}{4} \)
Calculating \( 2 \cdot \frac{9}{4} \):

\[ 2 \cdot \frac{9}{4} = \frac{18}{4} = \frac{9}{2} \]

### Step 5: Rewrite the equation
Now our equation looks like:

\[ \frac{9}{2} + \frac{3p}{2} - 6 = 0 \]

### Step 6: Eliminate the fraction by multiplying through by 2
To eliminate the fractions, we multiply the entire equation by 2:

\[ 9 + 3p - 12 = 0 \]

### Step 7: Simplify the equation
Now simplify the equation:

\[ 3p - 3 = 0 \]

### Step 8: Solve for \( p \)
Adding 3 to both sides gives:

\[ 3p = 3 \]

Dividing by 3:

\[ p = 1 \]

### Final Answer
Thus, the value of \( p \) is:

\[ \boxed{1} \]