8z^2=6z^2+38
\small{\text{ $ \begin{array}{rcl} 8z^2 &=& 6z^2+38 \quad | \quad -6z^2 \\ 8z^2-6z^2 &=& 38 \\ (8-6)z^2 &=& 38 \\ 2z^2 &=& 38 \quad | \quad :2 \\\\ z^2 &=& \dfrac{38}{2} \\\\ z^2 &=& 19\quad | \quad \pm\sqrt \\ z_{1,2} &=& \pm\sqrt{19} \\ \end{array} $ }} $\\\\$ \small{\text{ $ z_1 &=& 4.35889894354 $ and $ z_2 &=& -4.35889894354 $ }}
8z^2=6z^2+38
\small{\text{ $ \begin{array}{rcl} 8z^2 &=& 6z^2+38 \quad | \quad -6z^2 \\ 8z^2-6z^2 &=& 38 \\ (8-6)z^2 &=& 38 \\ 2z^2 &=& 38 \quad | \quad :2 \\\\ z^2 &=& \dfrac{38}{2} \\\\ z^2 &=& 19\quad | \quad \pm\sqrt \\ z_{1,2} &=& \pm\sqrt{19} \\ \end{array} $ }} $\\\\$ \small{\text{ $ z_1 &=& 4.35889894354 $ and $ z_2 &=& -4.35889894354 $ }}