Solve {l}{yleq5x^2-5x+3}{yleq-7x^2+6x+1}

$$\left\{ \begin{array} { l } { y \leq 5 x ^ { 2 } - 5 x + 3 } \\ { y \leq - 7 x ^ { 2 } + 6 x + 1 } \end{array} \right.$$

Solve for x

$$\left\{\begin{matrix}x\in \begin{bmatrix}\frac{\sqrt{20y-35}}{10}+\frac{1}{2},\frac{\sqrt{16-7y}+3}{7}\end{bmatrix}\text{, }&\frac{\sqrt{20y-35}}{10}+\frac{1}{2}\leq \frac{\sqrt{16-7y}+3}{7}\text{ and }y\geq \frac{7}{4}\text{ and }y<\frac{16}{7}\\x=\frac{3}{7}\approx 0.428571429\text{, }&y\leq \frac{87}{49}\\x\in \begin{bmatrix}\frac{-\sqrt{16-7y}+3}{7},-\frac{\sqrt{20y-35}}{10}+\frac{1}{2}\end{bmatrix}\text{, }&\frac{-\sqrt{16-7y}+3}{7}\leq -\frac{\sqrt{20y-35}}{10}+\frac{1}{2}\text{ and }\frac{\sqrt{16-7y}+3}{7}\geq -\frac{\sqrt{20y-35}}{10}+\frac{1}{2}\text{ and }y\geq \frac{7}{4}\text{ and }y<\frac{16}{7}\\x\in \begin{bmatrix}\frac{-\sqrt{16-7y}+3}{7},\frac{\sqrt{16-7y}+3}{7}\end{bmatrix}\text{, }&y\leq \frac{7}{4}\text{ or }\left(\frac{\sqrt{16-7y}+3}{7}<-\frac{\sqrt{20y-35}}{10}+\frac{1}{2}\text{ and }y\geq \frac{7}{4}\text{ and }y<\frac{16}{7}\right)\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y\leq \left(1-x\right)\left(7x+1\right)\text{, }&x\leq \frac{1}{4}\text{ or }x\geq \frac{2}{3}\\y\leq 5x^{2}-5x+3\text{, }&x>\frac{1}{4}\text{ and }x<\frac{2}{3}\end{matrix}\right.$$