Can we use The Black-Scholes Formulas to calculate American calls? If can't, why the model answers said they are the same?

And how to find N(x) and N(-x) in the formula?

Problem 13.26. Consider an option on a non-dividend-paying stock when the stock price is $30, the exe price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum the time to maturity is four months. a. What is the price of the option if it is a European call? b. What is the price of the option if it is an American call? c. What is the price of the option if it is a European put? d. Verify that put-call parity holds. In this case Sn = 30, K = 29, r=0.05, o=0.25 and T = 4/12 In(30/29)+(0.05+0.252 /2)4/12 d = -= 0.4225 0.25 0.3333 d, In(30/29)+(0.05 -0.25? / 2)x4/12 = 0.2782 0.250.3333 N(0.4225) = 0.6637, N(0.2782) = 0.6096 N(-0.4225) = 0.3363, N(-0.2782) = 0.3904 a. The European call price is 30x0.6637 - 29e0.05x4/12 *0.6096 = 2.52 b. The American call price is the same as the European call price. It is $2.52. The Luropean pur price is