Solve x^3+x-1+2a/a=0

$$\frac { x ^ { 3 } + x - 1 + 2 a } { a } = 0$$

Solve for a

$$a=\frac{1-x-x^{3}}{2}$$

$$x\neq \sqrt[3]{\frac{\sqrt{93}}{18}+\frac{1}{2}}+\sqrt[3]{-\frac{\sqrt{93}}{18}+\frac{1}{2}}\text{ and }x\neq \frac{18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{93}+9}+\sqrt[3]{9-\sqrt{93}}\right)}{18}$$

Steps for Solving Linear Equation

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

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

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

$$x-1+2a=-x^{3}$$

Subtract x from both sides.

$$-1+2a=-x^{3}-x$$

Add 1 to both sides.

$$2a=-x^{3}-x+1$$

The equation is in standard form.

$$2a=1-x-x^{3}$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{1-x-x^{3}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{1-x-x^{3}}{2}$$

Variable a cannot be equal to 0.

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

Solve for x

$$x=\frac{\sqrt[3]{3}\times 2^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{3\left(108a^{2}-108a+31\right)}-18a+9}+\sqrt[3]{-\sqrt{3\left(108a^{2}-108a+31\right)}-18a+9}\right)}{6}$$

$$a\neq 0$$