Solve B=pi/3y(R^2+R(67-y/16)+(67-y/16)^2)

$$B = \frac { \pi } { 3 } y ( R ^ { 2 } + R ( \frac { 67 - y } { 16 } ) + ( \frac { 67 - y } { 16 } ) ^ { 2 } )$$

Solve for R (complex solution)

$$\left\{\begin{matrix}R=\frac{\sqrt{-3y^{4}+402y^{3}+\frac{3072By}{\pi }-13467y^{2}}}{32y}+\frac{y}{32}-\frac{67}{32}\text{; }R=-\frac{\sqrt{-3y^{4}+402y^{3}+\frac{3072By}{\pi }-13467y^{2}}}{32y}+\frac{y}{32}-\frac{67}{32}\text{, }&y\neq 0\\R\in \mathrm{C}\text{, }&B=0\text{ and }y=0\end{matrix}\right.$$

Solve for B

$$B=\frac{\pi y\left(16R\left(67-y\right)+\left(67-y\right)^{2}+256R^{2}\right)}{768}$$

Solve for R

$$\left\{\begin{matrix}R=\frac{\sqrt{-3y^{4}+402y^{3}+\frac{3072By}{\pi }-13467y^{2}}}{32y}+\frac{y}{32}-\frac{67}{32}\text{; }R=-\frac{\sqrt{-3y^{4}+402y^{3}+\frac{3072By}{\pi }-13467y^{2}}}{32y}+\frac{y}{32}-\frac{67}{32}\text{, }&y\neq 0\text{ and }\left(y>0\text{ or }B\leq \frac{\pi y^{3}}{1024}-\frac{67\pi y^{2}}{512}+\frac{4489\pi y}{1024}\right)\text{ and }\left(y<0\text{ or }B\geq \frac{\pi y^{3}}{1024}-\frac{67\pi y^{2}}{512}+\frac{4489\pi y}{1024}\right)\\R\in \mathrm{R}\text{, }&B=0\text{ and }y=0\end{matrix}\right.$$