Step-by-Step Solution:
1. Rearrange the equation into standard form:

Subtract 48 from both sides:

$$
\(2 x^2-20 x-48=0\)
$$

2. Simplify the equation:

Notice that all terms are divisible by 2 . Divide the entire equation by 2 to make factoring easier:

$$
\(x^2-10 x-24=0\)
$$

3. Factor the quadratic expression:

We need to find two numbers that multiply to -24 and add to -10 .
- The factors of -24 are $\((-12,2),(-8,3)\)$, and $\((-6,4)\)$.
- The pair that adds up to -10 is -12 and 2 .

So, the factored form is:

$$
\((x-12)(x+2)=0\)
$$

4. Solve for $x$ :

Set each factor to zero:
- $\(x-12=0 \Rightarrow x=12\)$
- $\(x+2=0 \Rightarrow x=-2\)$

Check the Options:
The roots are 12 and -2 . Looking at the choices provided:
A. -4
B. 2
C. 6
D. 8
E. 12

Correct Option:
E. 12