To solve the equation x\(^2\) - 2x - 3 = 0, we can use the quadratic formula, which is given by:
x = (-b ± sqrt(b\^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax\^2 + bx + c = 0.
Using the coefficients of the given equation, a=1, b=-2, and c=-3, we get:
x = (-(-2) ± sqrt((-2)\^2 - 4(1)(-3))) / 2(1)
x = (2 ± sqrt(16)) / 2
x = (2 ± 4) / 2
So the solutions of the equation are:
x = 3 or x = -1
Therefore, the correct answer is: (-1, 3).