Solve {l}{a*a-f=15}{f+c=6}{c*a-e=13}

$$\left. \begin{array} { l } { a \times a - f = 15 } \\ { f + c = 6 } \\ { c \times a - e = 13 } \end{array} \right.$$

Solve for a, f, c

$$a=\sqrt{7}\left(\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})+\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\right)\approx 4.148640912\text{, }f=7\left(\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})+\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\right)^{2}-15\approx 2.211221419\text{, }c=7\left(-\left(\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})+\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\right)^{2}+3\right)\approx 3.788778581$$

$$a=-2\sqrt{7}\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\approx -4.918891414\text{, }f=28\left(\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\right)^{2}-15\approx 9.195492745\text{, }c=7\left(-4\left(\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\right)^{2}+3\right)\approx -3.195492745$$

$$a=\sqrt{7}\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})-\sqrt{21}\sin(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\approx 0.770250502\text{, }f=7\left(-\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})+\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\right)^{2}-15\approx -14.406714164\text{, }c=7\left(-\left(-\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})+\cos(\frac{\arccos(\frac{\sqrt{7}\left(e+13\right)}{98})}{3})\right)^{2}+3\right)\approx 20.406714164$$