f(x) is notation for a function. for example:
f(x) = x^2 could be an equation.
f(2) would be 2^2 = 4
you can write iterative equations like Jadz did above, with different X's (ie x1 x2 x3) usually in mathbooks the numbers are subscripted, which makes em a bit easier to read, but this'll work, for quick and dirty math example.
so, in her example, x0 is your initial guess.
x1 is the next iteration of the equation that will get closer and closer to the answer. so this:
x1 = x0 - f(x0)/f'(x0) in english, reads
the next iteration (x1) is equal to x0, minus a function using x0 as it's variable, divided by the derivative of that function, also using x0 as it's variable.
since f(x) = x^3 - 86 and
f'(x) (the derivative of f(x)) = x^2, that equation becomes:
x1 = x0 - ((x0^3 - 86)/x0^2)
it's 2 am so I hope that made sense/ was helpful!
