In d above equation which is given 1/2 n2-3n=Theta(n2) d leading coefficient is 1/2 coz n2 is of highest degree here. So certainly d answer will depend on more of d leading term. Yeah and 1/2 being d coefficient of n2. In essence n2 is of highest order and n only has order 1.Now d ques comes of determining d values of constants c1 and c2 respectively.
For d right hand side equality part as regards value of c2 is concerned it is 1/2 coz it is d coefficient of d highest degree. Therefore value of c2 is 1/2 and n is greater than or equal to 1. This covers d right hand side equality part.
However I m not able to understand how c1 has come as 1/14 for d left hand side inequality part. This then too solves 3/4th of ur explanation.