Atrisiniet P(x)=3x^2-10x-6quadD(x)=x-3

$$P ( x ) = 3 x ^ { 2 } - 10 x - 6 \quad D ( x ) = x - 3$$

Atrast D

$$D=\frac{x}{2}-\frac{11}{6}+\frac{1}{2x}$$

$$x\neq 0$$

Lineāra vienādojuma risināšanas darbības

Atņemiet 3x^{2} no abām pusēm.

$$-10x-6Dx=x-3-3x^{2}$$

Pievienot 10x abās pusēs.

$$-6Dx=x-3-3x^{2}+10x$$

Savelciet x un 10x, lai iegūtu 11x.

$$-6Dx=11x-3-3x^{2}$$

Vienādojums ir standarta formā.

$$\left(-6x\right)D=-3x^{2}+11x-3$$

Daliet abas puses ar -6x.

$$\frac{\left(-6x\right)D}{-6x}=\frac{-3x^{2}+11x-3}{-6x}$$

Dalīšana ar -6x atsauc reizināšanu ar -6x.

$$D=\frac{-3x^{2}+11x-3}{-6x}$$

Daliet 11x-3-3x^{2} ar -6x.

$$D=\frac{x}{2}-\frac{11}{6}+\frac{1}{2x}$$

Atrast x (complex solution)

$$x=\frac{\sqrt{36D^{2}+132D+85}}{6}+D+\frac{11}{6}$$

$$x=-\frac{\sqrt{36D^{2}+132D+85}}{6}+D+\frac{11}{6}$$

Atrast x

$$x=\frac{\sqrt{36D^{2}+132D+85}}{6}+D+\frac{11}{6}$$

$$x=-\frac{\sqrt{36D^{2}+132D+85}}{6}+D+\frac{11}{6}\text{, }D\leq -\frac{17}{6}\text{ or }D\geq -\frac{5}{6}$$