TeX source:
\begin{array}{rclcl} \dfrac{2x^2-3}{3} &=& \dfrac{1}{5} (x^2-8)+\dfrac{1}{3} &\vert& \cdot 3 \cdot 5 \cr\cr 5(2x^2-3) &=& 3(x^2-8)+5 \cr 10x^2-15 &=& 3x^2-24+5 &\vert& -3x^2+15 \cr 7x^2 &=& -4 &\vert& :7 \cr x^2 &=& -\dfrac{4}{7} &\vert& \pm\sqrt{} \cr\cr x_{1,2} &=& \pm\sqrt{-\dfrac{4}{7}} \end{array}