Solve {l}{7a^2-15b^2+6abc=0}{7a^2+8b^2-16abc=0}

$$\left\{ \begin{array} { l } { 7 a ^ { 2 } - 15 b ^ { 2 } + 6 a b c = 0 } \\ { 7 a ^ { 2 } + 8 b ^ { 2 } - 16 a b c = 0 } \end{array} \right.$$

Solve for a, b, c

$$\left\{\begin{matrix}\\a=0\text{, }b=0\text{, }c\in \mathrm{C}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }b=-\frac{\sqrt{462}a}{24}\text{, }c=-\frac{23\sqrt{462}}{528}\approx -0.936299737\text{; }a\in \mathrm{C}\text{, }b=\frac{\sqrt{462}a}{24}\text{, }c=\frac{23\sqrt{462}}{528}\approx 0.936299737\text{, }&\left(|arg(\frac{i\sqrt{-a}\sqrt{a}}{462})-arg(-a)|<\pi \text{ and }|arg(\frac{i\sqrt{-a}\sqrt{a}}{213444})-arg(-a)|<\pi \right)\text{ or }\left(|arg(\frac{i\sqrt{-a}\sqrt{a}}{462})-arg(a)|<\pi \text{ and }|arg(\frac{i\sqrt{-a}\sqrt{a}}{213444})-arg(a)|<\pi \right)\end{matrix}\right.$$