To solve this equation, we need to distribute on both sides and then combine like terms.

-x(1/3) - x^2 = x^2 - 1

Add x^2 to both sides:

x^2 - x^2/3 - x = -1

x^2 - 1/3 x - x + 1 = 0

x^2 - 4/3 x + 1 = 0

Now we have a quadratic equation that we can solve using the quadratic formula.

x = (-(-4/3) ± √((-4/3)^2 - 4(1)(1))) / 2(1)

x = (4/3 ± √(16/9 - 4)) / 2

x = (4/3 ± √(16/9 - 36/9)) / 2

x = (4/3 ± √(-20/9)) / 2

x = (4/3 ± 2√5i/3) / 2

x = (4 ± 2√5i) / 3

Therefore, the solutions to the equation are x = (4 + 2√5i) / 3 and x = (4 - 2√5i) / 3.