Solve {left(7/4yright)}^2+{left(y-7/4sqrt{sqrt{x^2}}right)}^2=1

$${ \left( \frac{ 7 }{ 4 } y \right) }^{ 2 } + { \left(y- \frac{ 7 }{ 4 } \sqrt{ \sqrt{ { x }^{ 2 } } } \right) }^{ 2 } =1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&y=-\frac{4\sqrt{65}}{65}\text{ or }y=\frac{4\sqrt{65}}{65}\\x=-\frac{\left(-\sqrt{16-49y^{2}}+4y\right)^{2}}{49}\text{; }x=\frac{\left(-\sqrt{16-49y^{2}}+4y\right)^{2}}{49}\text{, }&arg(\frac{-\sqrt{16-49y^{2}}+4y}{7})<\frac{\pi }{2}\\x=-\frac{\left(\sqrt{16-49y^{2}}+4y\right)^{2}}{49}\text{; }x=\frac{\left(\sqrt{16-49y^{2}}+4y\right)^{2}}{49}\text{, }&arg(\frac{\sqrt{16-49y^{2}}+4y}{7})<\frac{\pi }{2}\end{matrix}\right.$$

Solve for y (complex solution)

$$y=\frac{\sqrt{-2401\sqrt{x^{2}}+1040}+28\sqrt[4]{x^{2}}}{65}$$

$$y=\frac{-\sqrt{-2401\sqrt{x^{2}}+1040}+28\sqrt[4]{x^{2}}}{65}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\left(-\sqrt{16-49y^{2}}+4y\right)^{2}}{49}\text{; }x=-\frac{\left(-\sqrt{16-49y^{2}}+4y\right)^{2}}{49}\text{, }&\frac{-\sqrt{16-49y^{2}}+4y}{7}\geq 0\text{ and }|y|\leq \frac{4}{7}\\x=\frac{\left(\sqrt{16-49y^{2}}+4y\right)^{2}}{49}\text{; }x=-\frac{\left(\sqrt{16-49y^{2}}+4y\right)^{2}}{49}\text{, }&\frac{\sqrt{16-49y^{2}}+4y}{7}\geq 0\text{ and }|y|\leq \frac{4}{7}\end{matrix}\right.$$

Solve for y

$$y=\frac{\sqrt{-2401|x|+1040}+28\sqrt{|x|}}{65}$$

$$y=\frac{-\sqrt{-2401|x|+1040}+28\sqrt{|x|}}{65}\text{, }|x|\leq \frac{1040}{2401}$$