Atrisiniet fm^2-14m-15=0

$$f m ^ { 2 } - 14 m - 15 = 0$$

Atrast f

$$f=\frac{14m+15}{m^{2}}$$

$$m\neq 0$$

Lineāra vienādojuma risināšanas darbības

Pievienot 14m abās pusēs. Jebkuram skaitlim pieskaitot nulli, iegūst to pašu skaitli.

$$fm^{2}-15=14m$$

Pievienot 15 abās pusēs.

$$fm^{2}=14m+15$$

Vienādojums ir standarta formā.

$$m^{2}f=14m+15$$

Daliet abas puses ar m^{2}.

$$\frac{m^{2}f}{m^{2}}=\frac{14m+15}{m^{2}}$$

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

$$f=\frac{14m+15}{m^{2}}$$

Atrast m (complex solution)

$$\left\{\begin{matrix}m=\frac{\sqrt{15f+49}+7}{f}\text{; }m=\frac{-\sqrt{15f+49}+7}{f}\text{, }&f\neq 0\\m=-\frac{15}{14}\text{, }&f=0\end{matrix}\right,$$

Atrast m

$$\left\{\begin{matrix}m=\frac{\sqrt{15f+49}+7}{f}\text{; }m=\frac{-\sqrt{15f+49}+7}{f}\text{, }&f\neq 0\text{ and }f\geq -\frac{49}{15}\\m=-\frac{15}{14}\text{, }&f=0\end{matrix}\right,$$