reordering
[tex]\begin{gathered} 7x=3x^2-1 \\ 7x-7x=3x^2-1-7x \\ 3x^2-7x-1=0 \end{gathered}[/tex]then solve
[tex]\begin{gathered} x_{1,\: 2}=\frac{-\left(-7\right)\pm\sqrt{\left(-7\right)^2-4\cdot\:3\left(-1\right)}}{2\cdot\:3} \\ x_{1,\: 2}=\frac{-\left(-7\right)\pm\sqrt{61}}{2\cdot\:3} \\ x_1=\frac{-\left(-7\right)+\sqrt{61}}{2\cdot\:3},\: x_2=\frac{-\left(-7\right)-\sqrt{61}}{2\cdot\:3} \\ for\text{ one} \\ x=\frac{-(-7)+\sqrt[]{61}}{2\cdot\: 3}=\frac{7+\sqrt[]{61}}{6} \\ or \\ x=\frac{-(-7)-\sqrt[]{61}}{2\cdot\: 3}=\frac{7-\sqrt[]{61}}{6} \end{gathered}[/tex]answer:
[tex]\begin{gathered} x=\frac{7+\sqrt{61}}{6} \\ or \\ x=\frac{7-\sqrt{61}}{6} \end{gathered}[/tex]