Solve f(x)^prime=2x+6/5x^2

$$f ( x ) ^ { \prime } = \frac { 2 x + 6 } { 5 x ^ { 2 } }$$

Solve for f

$$f=\frac{2\left(x+3\right)}{5x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5x^{2}.

$$f\frac{\mathrm{d}}{\mathrm{d}x}(x)\times 5x^{2}=2x+6$$

Reorder the terms.

$$5fx^{2}\frac{\mathrm{d}}{\mathrm{d}x}(x)=2x+6$$

The equation is in standard form.

$$5x^{2}f=2x+6$$

Divide both sides by 5x^{2}.

$$\frac{5x^{2}f}{5x^{2}}=\frac{2x+6}{5x^{2}}$$

Dividing by 5x^{2} undoes the multiplication by 5x^{2}.

$$f=\frac{2x+6}{5x^{2}}$$

Divide 6+2x by 5x^{2}.

$$f=\frac{2\left(x+3\right)}{5x^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{30f+1}+1}{5f}\text{; }x=\frac{-\sqrt{30f+1}+1}{5f}\text{, }&f\neq 0\text{ and }f\geq -\frac{1}{30}\\x=-3\text{, }&f=0\end{matrix}\right.$$