To determine how many solutions the quadratic equation \(x^2 - x = 12\) has, we first rearrange it into standard form:
\[ x^2 - x - 12 = 0 \]
Next, we can analyze the quadratic equation \(ax^2 + bx + c = 0\) where \(a = 1\), \(b = -1\), and \(c = -12\). To find the number of solutions, we can calculate the discriminant \(D\) using the formula:
\[ D = b^2 - 4ac \]
Substituting the values of \(a\), \(b\), and \(c\):
\[ D = (-1)^2 - 4(1)(-12) = 1 + 48 = 49 \]
Since the discriminant \(D\) is positive (\(49\)), it indicates that the quadratic equation has two distinct real solutions.
Therefore, the correct statement is:
Statement #2: The equation has two solutions.