Solve {l}{z_{1}+frac{v_{1}*v_2^2}{2}=z_{2}+frac{v_{2}}{2}}{v_{1}=3}{z_{1}=5}{z_{2}=10}

$$\left. \begin{array} { l } { z _ { 1 } + \frac { v _ { 1 } \cdot v _ { 2 } ^ { 2 } } { 2 } = z _ { 2 } + \frac { v _ { 2 } } { 2 } } \\ { v _ { 1 } = 3 } \\ { z _ { 1 } = 5 } \\ { z _ { 2 } = 10 } \end{array} \right.$$

Solve for z_1, v_1, v_2, z_2

$$z_{1}=5\text{, }v_{1}=3\text{, }v_{2}=\frac{1-\sqrt{241}}{12}\approx -1.210347891\text{, }z_{2}=10$$

$$z_{1}=5\text{, }v_{1}=3\text{, }v_{2}=\frac{\sqrt{241}+1}{12}\approx 1.377014558\text{, }z_{2}=10$$