7 \sqrt { x } d y = 3 d
Solve for d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=\frac{9}{49y^{2}}\text{ and }arg(\sqrt{\frac{1}{y^{2}}}y)<\pi \text{ and }y\neq 0\end{matrix}\right.
Solve for d
\left\{\begin{matrix}d=0\text{, }&x\geq 0\\d\in \mathrm{R}\text{, }&y>0\text{ and }x=\frac{9}{49y^{2}}\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{9}{49y^{2}}\text{, }&y>0\\x\geq 0\text{, }&d=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{9}{49y^{2}}\text{, }&arg(\sqrt{\frac{1}{y^{2}}}y)<\pi \text{ and }y\neq 0\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.
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7\sqrt{x}dy-3d=0
Subtract 3d from both sides.
\left(7\sqrt{x}y-3\right)d=0
Combine all terms containing d.
d=0
Divide 0 by 7\sqrt{x}y-3.
7\sqrt{x}dy-3d=0
Subtract 3d from both sides.
\left(7\sqrt{x}y-3\right)d=0
Combine all terms containing d.
d=0
Divide 0 by 7\sqrt{x}y-3.
\frac{7dy\sqrt{x}}{7dy}=\frac{3d}{7dy}
Divide both sides by 7dy.
\sqrt{x}=\frac{3d}{7dy}
Dividing by 7dy undoes the multiplication by 7dy.
\sqrt{x}=\frac{3}{7y}
Divide 3d by 7dy.
x=\frac{9}{49y^{2}}
Square both sides of the equation.
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