Solve x^2+2x/Delta=3

$$x ^ { 2 } + \frac { 2 x } { \Delta } = 3$$

Solve for Δ (complex solution)

$$\Delta =-\frac{2x}{x^{2}-3}$$

$$x\neq 0\text{ and }x\neq -\sqrt{3}\text{ and }x\neq \sqrt{3}$$

Steps for Solving Linear Equation

Variable \Delta cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by \Delta .

$$\Delta x^{2}+2x=3\Delta$$

Subtract 3\Delta from both sides.

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

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$\Delta x^{2}-3\Delta =-2x$$

Combine all terms containing \Delta .

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

Divide both sides by x^{2}-3.

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

Dividing by x^{2}-3 undoes the multiplication by x^{2}-3.

$$\Delta =-\frac{2x}{x^{2}-3}$$

Variable \Delta cannot be equal to 0.

$$\Delta =-\frac{2x}{x^{2}-3}\text{, }\Delta \neq 0$$

Solve for Δ

$$\Delta =-\frac{2x}{x^{2}-3}$$

$$x\neq 0\text{ and }|x|\neq \sqrt{3}$$

Steps for Solving Linear Equation

Variable \Delta cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by \Delta .

$$\Delta x^{2}+2x=3\Delta$$

Subtract 3\Delta from both sides.

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

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$\Delta x^{2}-3\Delta =-2x$$

Combine all terms containing \Delta .

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

Divide both sides by x^{2}-3.

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

Dividing by x^{2}-3 undoes the multiplication by x^{2}-3.

$$\Delta =-\frac{2x}{x^{2}-3}$$

Variable \Delta cannot be equal to 0.

$$\Delta =-\frac{2x}{x^{2}-3}\text{, }\Delta \neq 0$$

Solve for x

$$x=\frac{\sqrt{3\Delta ^{2}+1}-1}{\Delta }$$

$$x=-\frac{\sqrt{3\Delta ^{2}+1}+1}{\Delta }\text{, }\Delta \neq 0$$