Given

#color(white)("XXX")sqrt(9x+10)=x#

Square both sides (this where an extraneous solution might be introduced)

#color(white)("XXX")9x+10=x^2#

Rearrange as a quadratic in standard form

#color(white)("XXX")x^2-9x-10=0#

Factor

#color(white)("XXX")(x-10)(x+1)=0#

Either

#color(white)("XXX")(x-10)=0color(white)("XX")rarrcolor(white)("XX")x=10#

or

#color(white)("XXX")(x+1)=0color(white)("XX")rarrcolor(white)("XX")x=-1#

Checking against original equation:

#color(white)("XXX")#If #x=10#

#color(white)("XXXXXXX")sqrt(9x+10)=sqrt(9(10)+10)=sqrt(100)=10=x#

#color(white)("XXX")#This solution is valid.

#color(white)("XXX")#If # x=-1#

#color(white)("XXXXXX")sqrt(9x+10)=sqrt(9(-1)+10)=sqrt(1)=1=x#

#color(white)("XXX")#This solution is valid