cosX+2sinX=-根号5,求tan的值,我需要解题过程,最近数学学得好乱

tanx=sinx/cosx
tan^2x=sin^2x/cos^2x=(1-cos^2x)/cos^2x
cos^2x=1/(1+tan^2x)
cosx+2sinx=-5^(1/2)
1+2tanx=-5^(1/2)/cosx
1+4tanx+tan^2x=5(1+tan^2x)
tan^2x-4tanx+4=0
(tanx-2)^2=0
tanx=2