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.