in post 1, its a^7, in post its x^6 ?
the number of roots is equal to the highest exponent, so 7 roots and 6 roots, receptively
if all you want is a solution, then use Wolfram Alpha
type in something like "what are the roots of a^7-2a^5-a^2 = -1"
enter, and wait a little while
when i did it, Wolfram Alpha provided 3 real roots and 4 more roots as complex conjugates
it took about 10 seconds
side issue: exponentials involve the base of the natural logs, such as e^x,
or the base of the common logs, such as 10^x
the variable is in the exponent
these equations are polynomials - the exponents are integers