Two sample Z test for means
Let $\overline{x}_1$
be the mean of a random sample of size $n_1$ from a population with mean $\mu_1$ and variance $\sigma^2_1$ and $\overline{x}_2$
be the mean of a random sample of size $n_2$ from a population with mean $\mu_2$ and variance $\sigma^2_2$.
The hypothesis testing problem can be setup as one of the three situations:
Situation  Hypothesis Testing Problem 

Situation A :  $H_0: \mu_1=\mu_2$ against $H_a : \mu_1 < \mu_2$ (Lefttailed) 
Situation B :  $H_0: \mu_1=\mu_2$ against $H_a : \mu_1 > \mu_2$ (Righttailed) 
Situation C :  $H_0: \mu_1=\mu_2$ against $H_a : \mu_1 \neq \mu_2$ (Twotailed) 
Formula
The test statistic under $H_0 : \mu_1 = \mu_2$ is
$Z = \frac{(\overline{x}_1\overline{x}_2)(\mu_1\mu_2)}{SE(\overline{x}_1\overline{x}_2)}$
where,

$\overline{x}_1$
is the sample mean of first sample of size $n_1$, 
$\overline{x}_2$
is the sample mean of second sample of size $n_2$, 
$SE(\overline{x}_1\overline{x}_2) = \sqrt{\frac{\sigma^2_1}{n_1}+ \frac{\sigma^2_2}{n_2}}$`,
The test statistic $Z$ follows standard normal distribution $N(0,1)$.