Solve Delta2x^3-12x^2+24x=0

$$\Delta 2 x ^ { 3 } - 12 x ^ { 2 } + 24 x = 0$$

Solve for Δ_2 (complex solution)

$$\left\{\begin{matrix}\Delta _{2}=-\frac{12\left(2-x\right)}{x^{2}}\text{, }&x\neq 0\\\Delta _{2}\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 12x^{2} to both sides. Anything plus zero gives itself.

$$\Delta _{2}x^{3}+24x=12x^{2}$$

Subtract 24x from both sides.

$$\Delta _{2}x^{3}=12x^{2}-24x$$

The equation is in standard form.

$$x^{3}\Delta _{2}=12x^{2}-24x$$

Divide both sides by x^{3}.

$$\frac{x^{3}\Delta _{2}}{x^{3}}=\frac{12x\left(x-2\right)}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$\Delta _{2}=\frac{12x\left(x-2\right)}{x^{3}}$$

Divide 12x\left(-2+x\right) by x^{3}.

$$\Delta _{2}=\frac{12\left(x-2\right)}{x^{2}}$$

Solve for Δ_2

$$\left\{\begin{matrix}\Delta _{2}=-\frac{12\left(2-x\right)}{x^{2}}\text{, }&x\neq 0\\\Delta _{2}\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 12x^{2} to both sides. Anything plus zero gives itself.

$$\Delta _{2}x^{3}+24x=12x^{2}$$

Subtract 24x from both sides.

$$\Delta _{2}x^{3}=12x^{2}-24x$$

The equation is in standard form.

$$x^{3}\Delta _{2}=12x^{2}-24x$$

Divide both sides by x^{3}.

$$\frac{x^{3}\Delta _{2}}{x^{3}}=\frac{12x\left(x-2\right)}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$\Delta _{2}=\frac{12x\left(x-2\right)}{x^{3}}$$

Divide 12x\left(-2+x\right) by x^{3}.

$$\Delta _{2}=\frac{12\left(x-2\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{2\sqrt{9-6\Delta _{2}}+6}{\Delta _{2}}\text{; }x=\frac{-2\sqrt{9-6\Delta _{2}}+6}{\Delta _{2}}\text{, }&\Delta _{2}\neq 0\\x=2\text{, }&\Delta _{2}=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{2\sqrt{9-6\Delta _{2}}+6}{\Delta _{2}}\text{; }x=\frac{-2\sqrt{9-6\Delta _{2}}+6}{\Delta _{2}}\text{, }&\Delta _{2}\neq 0\text{ and }\Delta _{2}\leq \frac{3}{2}\\x=2\text{, }&\Delta _{2}=0\end{matrix}\right.$$