y = 6 \sqrt { x } d x
Solve for d
\left\{\begin{matrix}d=\frac{y}{6x^{\frac{3}{2}}}\text{, }&x>0\\d\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\left(\frac{36y}{d}\right)^{\frac{2}{3}}}{36}\text{, }&\left(y\geq 0\text{ and }d>0\right)\text{ or }\left(y\leq 0\text{ and }d<0\right)\\x\geq 0\text{, }&y=0\text{ and }d=0\end{matrix}\right.
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6\sqrt{x}dx=y
Swap sides so that all variable terms are on the left hand side.
6\sqrt{x}xd=y
The equation is in standard form.
\frac{6\sqrt{x}xd}{6\sqrt{x}x}=\frac{y}{6\sqrt{x}x}
Divide both sides by 6\sqrt{x}x.
d=\frac{y}{6\sqrt{x}x}
Dividing by 6\sqrt{x}x undoes the multiplication by 6\sqrt{x}x.
d=\frac{y}{6x^{\frac{3}{2}}}
Divide y by 6\sqrt{x}x.
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