Why doesn't the formula work when checking two ECDSA signatures? There are two generated ECDSA signatures

X - Private key

S  = ((Z  + (X * R)) / K) mod n

S` = ((Z` + (X * R`)) / K`) mod n


G - Base point, of order n;

R  = K  * G
R` = K` * G


Why is this formula not working?

C = K - K`

R = R` + (C * G)


Where exactly do I make a mistake?
In ECDSA, the R value in the signature is not the elliptic curve point $kG$, but instead only its x-coordinate, that is, an integer.

So, what do you mean by R' + (C*G)?  In particular, what do you mean by the operator +?

If you mean "the + is an integer modular addition, that is, we take the x-coordinate of the point $CG$, and then add it (modulo $n$) to $R'$", well, that'll give you an integer that's unrelated to $R$ (as $R$ and $R'$ are related as elliptic curve points not integers, and integer addition and elliptic curve operations have little to do with each other)

If you mean "the + is an elliptic curve addition, that is, we find one of the points with x-coordinate $R'$, and add it (using the elliptic curve addition operation) to the point $C\cdot G$), well, that'll work half the time; there are (usually) two elliptic curve points with x-coordinate $R'$, and it'll work if the one you pick just happens to be the original $R'$ point.