To solve the equation 2002x^2 - 2001x - 1 = 0, we can use the quadratic formula:

x = (-(-2001) ± √((-2001)^2 - 4(2002)(-1))) / 2(2002)
x = (2001 ± √(4004001 + 8008)) / 4004
x = (2001 ± √4004009) / 4004
x = (2001 ± 2001) / 4004

So the two possible solutions are:
x = (2001 + 2001) / 4004 = 4002 / 4004 = 1
x = (2001 - 2001) / 4004 = 0 / 4004 = 0

Therefore, the solutions to the equation 2002x^2 - 2001x - 1 = 0 are x = 1 and x = 0.