Op-Amp analysis without using op-amp gain
And I know that :
  $$V_-=V_+$$


This is not true for your circuit. 

This rule becomes true when you set up a circuit with negative feedback. Your circuit does not use negative feedback, so you can't use this rule.

In your circuit, \$v_{out}\$ will be approximately equal to the positive supply rail when \$v_{in}&gt;V_B\$.  \$v_{out}\$ will be approximately equal to the negative supply rail when \$v_{in}&lt;V_B\$. 

To know the output when \$v_{in}\$ is very close to \$V_B\$, you'd need to know the op-amp's gain and offset voltage. To analyze it for a quickly varying \$v_{in}(t)\$ you'd need to know more about the internal workings of the op-amp, its slew rate limit, etc.