Solve y=(x-a)sqrt{x}

$$y = ( x - a ) \sqrt { x }$$

Solve for a

$$\left\{\begin{matrix}a=x-\frac{y}{\sqrt{x}}\text{, }&x>0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-a by \sqrt{x}.

$$y=x\sqrt{x}-a\sqrt{x}$$

Swap sides so that all variable terms are on the left hand side.

$$x\sqrt{x}-a\sqrt{x}=y$$

Subtract x\sqrt{x} from both sides.

$$-a\sqrt{x}=y-x\sqrt{x}$$

Reorder the terms.

$$-\sqrt{x}a=-\sqrt{x}x+y$$

The equation is in standard form.

$$\left(-\sqrt{x}\right)a=-\sqrt{x}x+y$$

Divide both sides by -\sqrt{x}.

$$\frac{\left(-\sqrt{x}\right)a}{-\sqrt{x}}=\frac{y-x^{\frac{3}{2}}}{-\sqrt{x}}$$

Dividing by -\sqrt{x} undoes the multiplication by -\sqrt{x}.

$$a=\frac{y-x^{\frac{3}{2}}}{-\sqrt{x}}$$

Divide -x^{\frac{3}{2}}+y by -\sqrt{x}.

$$a=x-\frac{y}{\sqrt{x}}$$