Solve y=ax^2-4xsqrt{x}

$$y = a x ^ { 2 } - 4 x \sqrt { x }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{4x^{\frac{3}{2}}+y}{x^{2}}\text{, }&x>0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}-4x\sqrt{x}=y$$

Add 4x\sqrt{x} to both sides.

$$ax^{2}=y+4x\sqrt{x}$$

The equation is in standard form.

$$x^{2}a=4\sqrt{x}x+y$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{4x^{\frac{3}{2}}+y}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{4x^{\frac{3}{2}}+y}{x^{2}}$$

Divide y+4x^{\frac{3}{2}} by x^{2}.

$$a=\frac{4}{\sqrt{x}}+\frac{y}{x^{2}}$$