C (clang), 121 bytes

d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=(!sscanf(a,"%d",&d))?1:d;printf("%d",(x-(o>43?-y:y))/d);} 

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Spaces are handled except between d and N. Result is rounded Down

Following will round Up >N+0.5 to N+1 @133 Bytes

N,d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=!sscanf(a,"%d",&d)?1:d;N=(x-(o>43?-y:y))*2/d;printf("%d",N/2+N%2);} 

C (clang), 133 bytes

N,d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=!sscanf(a,"%d",&d)?1:d;N=(x-(o>43?-y:y))*2/d;printf("%d",N/2+N%2);} 

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This handles all spaces except between d and N.

[Removed wrong answer that rounds down]

C (clang), 121 bytes

d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=(!sscanf(a,"%d",&d))?1:d;printf("%d",(x-(o>43?-y:y))/d);} 

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Result is rounded Down

Following will round Up >N+0.5 to N+1 @133 Bytes

N,d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=!sscanf(a,"%d",&d)?1:d;N=(x-(o>43?-y:y))*2/d;printf("%d",N/2+N%2);} 

C (clang), 121 bytes

d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=(!sscanf(a,"%d",&d))?1:d;printf("%d",(x-(o>43?-y:y))/d);} 

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Spaces are handled except between d and N. Result is rounded Down

Following will round Up >N+0.5 to N+1 @133 Bytes

N,d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=!sscanf(a,"%d",&d)?1:d;N=(x-(o>43?-y:y))*2/d;printf("%d",N/2+N%2);} 

C (clang), 121 bytes

d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=(!sscanf(a,"%d",&d))?1:d;printf("%d",(x-(o>43?-y:y))/d);} 

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Result is rounded Down

C (clang), 121 bytes

d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=(!sscanf(a,"%d",&d))?1:d;printf("%d",(x-(o>43?-y:y))/d);} 

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Result is rounded Down

Following will round Up >N+0.5 to N+1 @133 Bytes

N,d,y,x,a[9],o;f(*s){sscanf(s," %[0-9N] %c %d = %d",a,&o,&y,&x);d=!sscanf(a,"%d",&d)?1:d;N=(x-(o>43?-y:y))*2/d;printf("%d",N/2+N%2);}