Solution :
I had faced the same error in the past while I was running Android Studio on my windows and after that I did research on the issue and I realized that I must start the HAXM installer manually so that I can use it:
I went to my Android SDK folder in my case it was C:\Users\[user's name]\AppData\Local\Android\Sdk\extras\intel\Hardware_Accelerated_Execution_Manager\
and there I found that intelhaxm-android.exe
file, I clicked on the file and allowed it to finish
The installation process after that I launched my avd
device again then it ran properly for me.
Hope this solution will help you in resolving your issues.