First, we can square both sides of the equation to get rid of the square root. This gives us:
(a - 3)^2 = -a
We can then expand the left-hand side to get:
a^2 - 6a + 9 = -a
Combining like terms, we get:
a^2 - 5a + 9 = 0
We can then factor this equation to get:
(a - 1)(a - 9) = 0
This means that a = 1 or a = 9.
However, we need to check both solutions to make sure they are valid. If we substitute a = 1 into the original equation, we get:
(1 - 3)/sqrt(1) = -sqrt(1)
This is not a valid equation, since the square root of 1 is 1 and 1 - 3 is not equal to -1.
If we substitute a = 9 into the original equation, we get:
(9 - 3)/sqrt(9) = -sqrt(9)
This is a valid equation, since the square root of 9 is 3 and 9 - 3 is equal to 6.
Therefore, the only solution to the equation is a = 9.
