Square both sides of equation, we have sqrt(3)-sqrt(sqrt(3)+x)=x^2.
sqrt(sqrt(3)+x)=sqrt(3)-x^2.
Square both sides of equation, we have sqrt(3)+x=(sqrt(3)-x^2)^2.
sqrt(3)+x=3-2sqrt(3)x^2+x^4
x^4-2sqrt(3)x^2-x+3-sqrt(3)=0
Then solve the quartic equation.
Square both sides of equation, we have sqrt(3)-sqrt(sqrt(3)+x)=x^2.
sqrt(sqrt(3)+x)=sqrt(3)-x^2.
Square both sides of equation, we have sqrt(3)+x=(sqrt(3)-x^2)^2.
sqrt(3)+x=3-2sqrt(3)x^2+x^4
x^4-2sqrt(3)x^2-x+3-sqrt(3)=0
Then solve the quartic equation.