Nextcloud version (eg, 12.0.2): 3.9.0
Operating system and version (eg, Ubuntu 17.04): android
The issue you are facing:
Hello, do you know if there is the possibily to consult/edit the calendar/agenda in the nextclous’s app on android ?
No that’s not possible . You have to install the DAVx5 app to sync calendar/calendar/task information with your device.
Ok…but this service is not free…
When using a classic calendar app , we can sync for free with microsoft or google account.
Why does nextcloud doesnt develop it for free ?
I can via my website browser be connected with nextclood, and i have the possibily to have acces at my calendar and edit it. I dont understand the difference between have acess for free on a web browser and pay using an app … if you can tell me the logik ?
First of all, development of Nextcloud and/or DAVx5 need to be financed somehow and 3,99 EUR/once off for a valuable app is worse it. Many people spend more than that for a box of cigarettes per day! Additionally you’re wrong with the assumption that Microsoft and Google are providing their apps for free, you trade-in your private data and that’s the way they earn many with their services 
And finally you 're wrong with the assumption that the DAVx5 app cannot be downloaded for free. You can find an official releases on F-droid, although I personally would vote to buy the app to honor the work of the developers.
Your reponse is 200% correct. You have confirmed my opinion too.
So, to use the fonctionnality and the synchronisation Davx5, i have to install in addition a software to consult my calendar ?
You can use the default apps for contacts and calendars, only for task you require an additiona all like OpenTasks.
Ok thank you j ed