Solve 122/9/x=frac{1+sqrt{5}}{2}

$$\frac{ \frac{ 122 }{ 9 } }{ x } = \frac{ 1+ \sqrt{ 5 } }{ 2 }$$

Solve for x

$$x = \frac{61 {(\sqrt{5} - 1)}}{9} \approx 8.37779407$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2.

$$2\times \frac{122}{9}=x\left(1+\sqrt{5}\right)$$

Express 2\times \frac{122}{9} as a single fraction.

$$\frac{2\times 122}{9}=x\left(1+\sqrt{5}\right)$$

Multiply 2 and 122 to get 244.

$$\frac{244}{9}=x\left(1+\sqrt{5}\right)$$

Use the distributive property to multiply x by 1+\sqrt{5}.

$$\frac{244}{9}=x+x\sqrt{5}$$

Swap sides so that all variable terms are on the left hand side.

$$x+x\sqrt{5}=\frac{244}{9}$$

Combine all terms containing x.

$$\left(1+\sqrt{5}\right)x=\frac{244}{9}$$

The equation is in standard form.

$$\left(\sqrt{5}+1\right)x=\frac{244}{9}$$

Divide both sides by 1+\sqrt{5}.

$$\frac{\left(\sqrt{5}+1\right)x}{\sqrt{5}+1}=\frac{\frac{244}{9}}{\sqrt{5}+1}$$

Dividing by 1+\sqrt{5} undoes the multiplication by 1+\sqrt{5}.

$$x=\frac{\frac{244}{9}}{\sqrt{5}+1}$$

Divide \frac{244}{9} by 1+\sqrt{5}.

$$x=\frac{61\sqrt{5}-61}{9}$$