Solve {l}{a_s^2+3a_{t}d+2d^2=28}{2a_{c}+5d=17}

$$\left\{ \begin{array} { l } { a _ { s } ^ { 2 } + 3 a _ { t } d + 2 d ^ { 2 } = 28 } \\ { 2 a _ { c } + 5 d = 17 } \end{array} \right.$$

Solve for a_s, a_t, d, a_c (complex solution)

$$a_{s}=\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}\in \mathrm{C}\text{, }d\in \mathrm{C}\text{, }a_{c}=\frac{17-5d}{2}$$

$$a_{s}=-\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}\in \mathrm{C}\text{, }d\in \mathrm{C}\text{, }a_{c}=\frac{17-5d}{2}$$

Solve for a_s, a_t, d, a_c

$$\left\{\begin{matrix}\\a_{s}=-\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}=-\frac{2d}{3}+\frac{28}{3d}\text{, }d\in \mathrm{R}\text{, }a_{c}=\frac{17-5d}{2}\text{; }a_{s}=\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}=-\frac{2d}{3}+\frac{28}{3d}\text{, }d\in \mathrm{R}\text{, }a_{c}=\frac{17-5d}{2}\text{; }a_{s}=-2\sqrt{7}\approx -5.291502622\text{, }a_{t}\in \mathrm{R}\text{, }d=0\text{, }a_{c}=\frac{17}{2}=8.5\text{; }a_{s}=2\sqrt{7}\approx 5.291502622\text{, }a_{t}\in \mathrm{R}\text{, }d=0\text{, }a_{c}=\frac{17}{2}=8.5\text{; }a_{s}=-\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}=-\frac{2d}{3}+\frac{28}{3d}\text{, }d<0\text{, }a_{c}=\frac{17-5d}{2}\text{; }a_{s}=-\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}\leq -\frac{2d}{3}+\frac{28}{3d}\text{, }d>0\text{, }a_{c}=\frac{17-5d}{2}\text{; }a_{s}=\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}=-\frac{2d}{3}+\frac{28}{3d}\text{, }d<0\text{, }a_{c}=\frac{17-5d}{2}\text{; }a_{s}=\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}\leq -\frac{2d}{3}+\frac{28}{3d}\text{, }d>0\text{, }a_{c}=\frac{17-5d}{2}\text{, }&\text{unconditionally}\\a_{s}=-\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}\geq -\frac{2d}{3}+\frac{28}{3d}\text{, }d<0\text{, }a_{c}=\frac{17-5d}{2}\text{; }a_{s}=\sqrt{28-2d^{2}-3a_{t}d}\text{, }a_{t}\geq -\frac{2d}{3}+\frac{28}{3d}\text{, }d<0\text{, }a_{c}=\frac{17-5d}{2}\text{, }&d\leq 0\end{matrix}\right.$$