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should x> 0
x*lnx=x-2 => lnx=(2-x)/x => lnx=ln(2-x)/x => x= (2-x)/x => x^2+x-2=0 ,Δ=1^2-4*(-2)*1=1+8=9
x=(-1*-3)/2 and x=(-1+3)/2 so x=1 and x=-2