Atrisiniet f2x^2-7x+6=0

$$f 2 x ^ { 2 } - 7 x + 6 = 0$$

Atrast f_2

$$f_{2}=-\frac{6-7x}{x^{2}}$$

$$x\neq 0$$

Lineāra vienādojuma risināšanas darbības

Pievienot 7x abās pusēs. Jebkuram skaitlim pieskaitot nulli, iegūst to pašu skaitli.

$$f_{2}x^{2}+6=7x$$

Atņemiet 6 no abām pusēm.

$$f_{2}x^{2}=7x-6$$

Vienādojums ir standarta formā.

$$x^{2}f_{2}=7x-6$$

Daliet abas puses ar x^{2}.

$$\frac{x^{2}f_{2}}{x^{2}}=\frac{7x-6}{x^{2}}$$

Dalīšana ar x^{2} atsauc reizināšanu ar x^{2}.

$$f_{2}=\frac{7x-6}{x^{2}}$$

Atrast x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{49-24f_{2}}+7}{2f_{2}}\text{; }x=\frac{-\sqrt{49-24f_{2}}+7}{2f_{2}}\text{, }&f_{2}\neq 0\\x=\frac{6}{7}\text{, }&f_{2}=0\end{matrix}\right,$$

Atrast x

$$\left\{\begin{matrix}x=\frac{\sqrt{49-24f_{2}}+7}{2f_{2}}\text{; }x=\frac{-\sqrt{49-24f_{2}}+7}{2f_{2}}\text{, }&f_{2}\neq 0\text{ and }f_{2}\leq \frac{49}{24}\\x=\frac{6}{7}\text{, }&f_{2}=0\end{matrix}\right,$$