\left\{ \begin{array} { l } { - \frac { 17 } { 4 } = - ( 1 + z ^ { 2 } - 4 a c ) } \\ { 5 = 4 a + 2 z + c } \\ { z = 2 a } \end{array} \right.
Solve for z, a, c
z=-\frac{\sqrt{217}}{18}+\frac{5}{9}\approx -0.262828881\text{, }a=-\frac{\sqrt{217}}{36}+\frac{5}{18}\approx -0.131414441\text{, }c=\frac{2\sqrt{217}+25}{9}\approx 6.051315525
z=\frac{\sqrt{217}}{18}+\frac{5}{9}\approx 1.373939992\text{, }a=\frac{\sqrt{217}}{36}+\frac{5}{18}\approx 0.686969996\text{, }c=\frac{25-2\sqrt{217}}{9}\approx -0.495759969
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