I know that for this statement :

"this equation x²=1 has 2 different solutions only"

the translation will be :

ƎxƎy( x²=1 ʌ y=1 ʌ x≠y ʌ ∀z( z²=1 → (z=xVy=y)).

now it might sound a bit dumb to ask, but what if the equation would be x²-1=2x ?

thanks.

p.s - feel free to correct my freely translated terms, ex : I'm not sure if you say translate or formalize... it would help me be clearer for further questions :))