Solve {c}{4ac-b^2/4a=1400}{a=-2}{b=280+2mquadc=-8000-200m}

$$\left. \begin{array} { c } { \frac { 4 a c - b ^ { 2 } } { 4 a } = 1400 } \\ { a = - 2 } \\ { b = 280 + 2 m \quad c = - 8000 - 200 m } \end{array} \right.$$

Solve for a, c, b, m (complex solution)

$$\left\{\begin{matrix}\\a=-2\text{, }c=-8400\text{, }b=280\text{, }m=0\text{; }a=-2\text{, }c=2800\left(-\sqrt{42}-6\right)\approx -34946.073955542\text{, }b=40\left(\sqrt{42}+7\right)\approx 539.229627936\text{, }m=-\frac{7-\sqrt{42}}{140}\approx -0.003708995\text{; }a=-2\text{, }c=2800\left(\sqrt{42}-6\right)\approx 1346.073955542\text{, }b=40\left(7-\sqrt{42}\right)\approx 20.770372064\text{, }m=-\frac{\sqrt{42}+7}{140}\approx -0.096291005\text{, }&\text{unconditionally}\\a=-2\text{, }c=\frac{11200-b^{2}}{8}\text{, }b\in \mathrm{C}\text{, }m=-\frac{4\left(280-b\right)}{11200-b^{2}}\text{, }&b\neq 280\text{ and }b\neq -40\sqrt{7}\text{ and }b\neq 40\sqrt{7}\text{ and }\left(arg(-\frac{2b\left(280-b\right)}{11200-b^{2}}+1)<\pi \text{ or }arg(\frac{b^{2}-560b+11200}{11200-b^{2}})\geq \pi \right)\end{matrix}\right.$$

Solve for a, c, b, m

$$a=-2\text{, }c=-8400\text{, }b=280\text{, }m=0$$

$$a=-2\text{, }c=-\frac{b^{2}}{8}+1400\text{, }b=\frac{-2\sqrt{2800m^{2}+280m+1}-2}{m}\text{, }m\in (-\infty,-\frac{\sqrt{42}}{140}-\frac{1}{20}]\cup [\frac{\sqrt{42}}{140}-\frac{1}{20},0)\cup (0,\infty)\text{; }a=-2\text{, }c=-\frac{b^{2}}{8}+1400\text{, }b=\frac{2\sqrt{2800m^{2}+280m+1}-2}{m}\text{, }m\in (-\infty,-\frac{\sqrt{42}}{140}-\frac{1}{20}]\cup [\frac{\sqrt{42}}{140}-\frac{1}{20},0)\cup (0,\infty)$$