Evaluate the Discriminant for the Equation $$5 a ^ { 3 } x ^ { 7 } \left( - 3 a ^ { 6 } x ^ { 8 } - 7 x ^ { 4 } - 8 a \right)$$

Multiple Choice

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
- $$5 a ^ { 3 } x ^ { 7 } \left( - 3 a ^ { 6 } x ^ { 8 } - 7 x ^ { 4 } - 8 a \right)$$

A) $- 15 a ^ { 18 } x ^ { 56 } + 35 a ^ { 3 } x ^ { 28 } + 40 a ^ { 3 } x ^ { 7 }$
B) $15 a ^ { 9 } x ^ { 15 } + 35 a ^ { 3 } x ^ { 11 } + 40 a ^ { 4 } x ^ { 7 }$
C) $- 15 a ^ { 9 } x ^ { 15 } - 7 x ^ { 4 } - 8 a$
D) $- 15 a ^ { 9 } x ^ { 15 } - 35 a ^ { 3 } x ^ { 11 } - 40 a ^ { 4 } x ^ { 7 }$