An indeterminate is simply a variable that is not known or solvable. It is usually denoted by a mathematical alphabet ($x$ $y$ $z$ or $\alpha$ $\beta$ etc...). It is important to distinguish between a variable and an indeterminate in that a variable is solvable, at least conditionally. To make this more precise, let's see two examples:

1. Let $x$ be a variable such that $2+3x=a+bx$ where $a,b\in\mathbb{Q}$ Then $x=(a-2)/(3-b)$ Here $x$ is solvable conditioned on the equation given. Any values of $a$ and $b\,(\neq 3)$ will yield a value for $x$
2. Let $x$ be an indeterminate such that $2+3x=a+bx$ where $a,\,b\in\mathbb{Q}$ Since $x$ can not be solved, we have $2=a$ , and $3=b$ Note that if $a$ and $b$ are previously assigned to be values other than 2 and 3 respectively, then $x$ is no longer an indeterminate.