Find a, b,c where 5x^2 + ax -7 = b(x+2)^2 + c
where a, b,c are constants

Expanding the right side:-

5x^2 + Ax - 7 = Bx^2 +4Bx  + 4B + C

Equating coefficients of x^2:-

B = 5

Equating coefficients of x:-

A = 4B 
so 
A = 4*5 = 20

Equating constants terms

-7 = 4B + C = 20 + C

C =  - 27

A=20 , B = 5 and C = -27

Aand b are correctly balanced reactions. they have the same number of atoms in both sides of the reaction