Solve for B (complex solution)
\left\{\begin{matrix}B=\frac{4y+3}{x^{2}}\text{, }&x\neq 0\\B\in \mathrm{C}\text{, }&y=-\frac{3}{4}\text{ and }x=0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=\frac{4y+3}{x^{2}}\text{, }&x\neq 0\\B\in \mathrm{R}\text{, }&y=-\frac{3}{4}\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-iB^{-\frac{1}{2}}\sqrt{-4y-3}\text{; }x=iB^{-\frac{1}{2}}\sqrt{-4y-3}\text{, }&B\neq 0\\x\in \mathrm{C}\text{, }&y=-\frac{3}{4}\text{ and }B=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\sqrt{\frac{4y+3}{B}}\text{; }x=-\sqrt{\frac{4y+3}{B}}\text{, }&\left(y\geq -\frac{3}{4}\text{ and }B>0\right)\text{ or }\left(y\leq -\frac{3}{4}\text{ and }B<0\right)\\x\in \mathrm{R}\text{, }&y=-\frac{3}{4}\text{ and }B=0\end{matrix}\right.
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Bx^{2}=3+4y
Add 4y to both sides.
x^{2}B=4y+3
The equation is in standard form.
\frac{x^{2}B}{x^{2}}=\frac{4y+3}{x^{2}}
Divide both sides by x^{2}.
B=\frac{4y+3}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
Bx^{2}=3+4y
Add 4y to both sides.
x^{2}B=4y+3
The equation is in standard form.
\frac{x^{2}B}{x^{2}}=\frac{4y+3}{x^{2}}
Divide both sides by x^{2}.
B=\frac{4y+3}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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