Solve F ∫ 0.2x-0.04=0.16x+0.28

$$F \int 0.2 x - 0.04 = 0.16 x + 0.28$$

Solve for F

$$\left\{\begin{matrix}F=\frac{4x+7}{25\left(\frac{x^{2}}{10}-\frac{x}{25}+С\right)}\text{, }&С\neq -\frac{x\left(x-0.4\right)}{10}\\F\in \mathrm{R}\text{, }&x=-\frac{7}{4}\text{ and }С=-\frac{301}{800}\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\left(\frac{x^{2}}{10}-\frac{x}{25}+С\right)F=\frac{4x+7}{25}$$

Divide both sides by \frac{1}{10}x^{2}-0.04x+С.

$$\frac{\left(\frac{x^{2}}{10}-\frac{x}{25}+С\right)F}{\frac{x^{2}}{10}-\frac{x}{25}+С}=\frac{4x+7}{25\left(\frac{x^{2}}{10}-\frac{x}{25}+С\right)}$$

Dividing by \frac{1}{10}x^{2}-0.04x+С undoes the multiplication by \frac{1}{10}x^{2}-0.04x+С.

$$F=\frac{4x+7}{25\left(\frac{x^{2}}{10}-\frac{x}{25}+С\right)}$$

Solve for x

$$\left\{\begin{matrix}\\x=-1.75\text{, }&\text{unconditionally}\\x=\frac{\sqrt{625СF^{2}+F^{2}+78F+16}+F+4}{5F}\text{; }x=\frac{-\sqrt{625СF^{2}+F^{2}+78F+16}+F+4}{5F}\text{, }&F\neq 0\text{ and }С\geq -\frac{1}{625}-\frac{78}{625F}-\frac{16}{625F^{2}}\end{matrix}\right.$$