To determine how many solutions the quadratic equation \( x^2 - x - 12 = 0 \) has, we can first rewrite the equation in standard form and then calculate the discriminant.
1. Rearranging the equation:
\[
x^2 - x - 12 = 0
\]
2. The discriminant \( D \) of a quadratic equation \( ax^2 + bx + c = 0 \) is calculated as:
\[
D = b^2 - 4ac
\]
where \( a = 1 \), \( b = -1 \), and \( c = -12 \).
3. Substituting in the values:
\[
D = (-1)^2 - 4(1)(-12) = 1 + 48 = 49
\]
The discriminant \( D = 49 \) is positive, which indicates that the quadratic equation has two distinct real solutions.
Therefore, the correct statement is:
**Statement #2: The equation has two solutions.**