Solve x^2x2+3x^2-6x-1=0

$${ x }^{ 2 } x2+3 { x }^{ 2 } -6x-1 = 0$$

Solve for x_2

$$x_{2}=-3+\frac{6}{x}+\frac{1}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

$$x^{2}x_{2}-6x-1=-3x^{2}$$

Add 6x to both sides.

$$x^{2}x_{2}-1=-3x^{2}+6x$$

Add 1 to both sides.

$$x^{2}x_{2}=-3x^{2}+6x+1$$

The equation is in standard form.

$$x^{2}x_{2}=1+6x-3x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}x_{2}}{x^{2}}=\frac{1+6x-3x^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$x_{2}=\frac{1+6x-3x^{2}}{x^{2}}$$

Divide -3x^{2}+6x+1 by x^{2}.

$$x_{2}=-3+\frac{6}{x}+\frac{1}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{x_{2}+12}+3}{x_{2}+3}\text{; }x=\frac{-\sqrt{x_{2}+12}+3}{x_{2}+3}\text{, }&x_{2}\neq -3\\x=-\frac{1}{6}\approx -0.166666667\text{, }&x_{2}=-3\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{x_{2}+12}+3}{x_{2}+3}\text{; }x=\frac{-\sqrt{x_{2}+12}+3}{x_{2}+3}\text{, }&x_{2}\neq -3\text{ and }x_{2}\geq -12\\x=-\frac{1}{6}\approx -0.166666667\text{, }&x_{2}=-3\end{matrix}\right.$$