How to solve a single inequality equation in R?

Question

I'm using Tim Gerrodette's inequality equation (1987), to look at power analysis of visual survey data, however i'm struggling of finding away to solve this for x, using R.

I have the following equation

r^2 * n^3 > 12*cv^2(za/2 + zB)^2

where r=0.02, n=40, cv=0.67, za/2=1.645, and I want to solve for zB (x, essentially) Which translates to:

0 < zB^2 + 3.3zB - 2.04 Where -3.4 < zB < 3.4

How might I go about solving this in R? I've looked at quadprog and limsolve, but i'm not sure that I'm on the right track as many seem to be using these functions to solve multiple/simultaneous equations.

I'm looking for a method in R that I can use, and sub in a series of values for r,n, CV etc.

Answer 1

If the question is how to obtain the set of values for which zB satisfies the 3 inequalities we can determine this up to 3 decimal places (or other by changing .001) using brute force so the interval shown below satisfies the inequalities.

zB <- seq(-3.4, 3.4, .001)
range(zB[zB > -3.4 & zB < 3.4 & zB^2 + 3.3 * zB > 2.04])
## [1] 0.533 3.399