Irrational equation algebra

If $x$ satisfy this equation: $x+\sqrt{x^4+x^2+1}=\sqrt{x-x^3}$ and $x=-\dfrac{a+\sqrt{b}}{c}$ and $a$ , $b$ , and $c$ are positive integers smaller than 10, find the three-digit number with $a$ in hundreds, $b$ in tens and $c$ in ones.