To find the discriminant of the given quadratic equation, we need to first write it in standard form, which is:
ax^2 + bx + c = 0
Rearranging the given equation, we get:
-x^2 - 8x + 12 = 0
Comparing this with the standard form, we see that:
a = -1, b = -8, c = 12
Now, we can use the formula for the discriminant, which is:
b^2 - 4ac
Substituting the values of a, b, and c, we get:
(-8)^2 - 4(-1)(12)
64 + 48
112
Therefore, the discriminant of the given quadratic equation is 112.