Consider the following polynomial equation:$(x^2+a)^2+a=x$Where $a$ is a real number such that the equation has four distinct real roots. If the difference between the largest and the smallest roots of equation is $7$, then $a$ can be written in the simplest form as:$-\frac{\overline{ABBB}}{\overline{ACC}}$Find the value of $A^2+B^2+C^2$.

**Details and Assumptions**:

$A$, $B$ and $C$ are some digits from $1$ to $9$.

As an explicit example, let's say that $-2$, $-1$, $0$ and $1$ are the roots of polynomial, then the largest root is $1$ and the smallest is $-2$ and the difference between them is $1-(-2)=3$.