$\,\,\,\,\,\,\,{{x}^{2}}+x+1=3\left( {{x}^{4}}+{{x}^{2}}+1 \right)$
$\Leftrightarrow 3{{x}^{4}}+3{{x}^{2}}+3-\left( {{x}^{2}}+x+1 \right)=0$
$\Leftrightarrow 3{{x}^{4}}+2{{x}^{2}}-x+2=0$
$\Leftrightarrow 3{{x}^{4}}+\left( 2{{x}^{2}}-x+\dfrac{1}{8} \right)+\dfrac{15}{8}$
$\Leftrightarrow 3{{x}^{4}}+{{\left( x\sqrt{2}+\dfrac{\sqrt{2}}{4} \right)}^{2}}+\dfrac{15}{8}>0$
$\to $phương trình vô nghiệm