Solve f(x)=ax^3-3/2+b(xinR)

$$f ( x ) = a x ^ { 3 } - 3 / 2 + b ( x \in R )$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{2b\left(x\in R\right)-2fx-3}{2x^{3}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=\frac{3}{2\left(0\in R\right)}\text{ and }x=0\text{ and }\left(0\in R\right)\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{3}-\frac{3}{2}+b\left(x\in R\right)=fx$$

Add \frac{3}{2} to both sides.

$$ax^{3}+b\left(x\in R\right)=fx+\frac{3}{2}$$

Subtract b\left(x\in R\right) from both sides.

$$ax^{3}=fx+\frac{3}{2}-b\left(x\in R\right)$$

Reorder the terms.

$$ax^{3}=-b\left(x\in R\right)+fx+\frac{3}{2}$$

The equation is in standard form.

$$x^{3}a=-b\left(x\in R\right)+fx+\frac{3}{2}$$

Divide both sides by x^{3}.

$$\frac{x^{3}a}{x^{3}}=\frac{-b\left(x\in R\right)+fx+\frac{3}{2}}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$a=\frac{-b\left(x\in R\right)+fx+\frac{3}{2}}{x^{3}}$$

Divide -b\left(x\in R\right)+fx+\frac{3}{2} by x^{3}.

$$a=\frac{-2b\left(x\in R\right)+2fx+3}{2x^{3}}$$