Solve 3x^2+4y^11=3x

$$3 x ^ { 2 } + 4 y ^ { 11 } = 3 x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{9-48y^{11}}}{6}+\frac{1}{2}$$

$$x=-\frac{\sqrt{9-48y^{11}}}{6}+\frac{1}{2}$$

Solve for y (complex solution)

$$y\in \frac{2^{\frac{9}{11}}e^{\frac{3\pi i}{11}}\sqrt[11]{x}\sqrt[11]{3\left(x-1\right)}}{2},\frac{2^{\frac{9}{11}}e^{\frac{\pi i}{11}}\sqrt[11]{x}\sqrt[11]{3\left(x-1\right)}}{2},\frac{2^{\frac{9}{11}}e^{\frac{5\pi i}{11}}\sqrt[11]{x}\sqrt[11]{3\left(x-1\right)}}{2},\frac{2^{\frac{9}{11}}e^{\frac{7\pi i}{11}}\sqrt[11]{3x}\sqrt[11]{x-1}}{2},\frac{2^{\frac{9}{11}}e^{\frac{9\pi i}{11}}\sqrt[11]{3x}\sqrt[11]{x-1}}{2},-\frac{4^{\frac{10}{11}}\sqrt[11]{3x}\sqrt[11]{x-1}}{4},\frac{2^{\frac{9}{11}}e^{\frac{13\pi i}{11}}\sqrt[11]{3x}\sqrt[11]{x-1}}{2},\frac{2^{\frac{9}{11}}e^{\frac{15\pi i}{11}}\sqrt[11]{3x}\sqrt[11]{x-1}}{2},\frac{2^{\frac{9}{11}}e^{\frac{17\pi i}{11}}\sqrt[11]{3x}\sqrt[11]{x-1}}{2},\frac{2^{\frac{9}{11}}e^{\frac{19\pi i}{11}}\sqrt[11]{3x}\sqrt[11]{x-1}}{2},\frac{2^{\frac{9}{11}}e^{\frac{21\pi i}{11}}\sqrt[11]{3x}\sqrt[11]{x-1}}{2}$$

Solve for x

$$x=\frac{\sqrt{9-48y^{11}}}{6}+\frac{1}{2}$$

$$x=-\frac{\sqrt{9-48y^{11}}}{6}+\frac{1}{2}\text{, }y\leq \frac{16^{\frac{10}{11}}\sqrt[11]{3}}{16}$$

Solve for y

$$y=-\frac{4^{\frac{10}{11}}\sqrt[11]{3x\left(x-1\right)}}{4}$$