Atrisiniet kx^2-5x=3

$$k x ^ { 2 } - 5 x = 3$$

Atrast k

$$k=\frac{5x+3}{x^{2}}$$

$$x\neq 0$$

Lineāra vienādojuma risināšanas darbības

Pievienot 5x abās pusēs.

$$kx^{2}=3+5x$$

Vienādojums ir standarta formā.

$$x^{2}k=5x+3$$

Daliet abas puses ar x^{2}.

$$\frac{x^{2}k}{x^{2}}=\frac{5x+3}{x^{2}}$$

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

$$k=\frac{5x+3}{x^{2}}$$

Atrast x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{12k+25}+5}{2k}\text{; }x=\frac{-\sqrt{12k+25}+5}{2k}\text{, }&k\neq 0\\x=-\frac{3}{5}\text{, }&k=0\end{matrix}\right,$$

Atrast x

$$\left\{\begin{matrix}x=\frac{\sqrt{12k+25}+5}{2k}\text{; }x=\frac{-\sqrt{12k+25}+5}{2k}\text{, }&k\neq 0\text{ and }k\geq -\frac{25}{12}\\x=-\frac{3}{5}\text{, }&k=0\end{matrix}\right,$$