Solve 2sqrt{5}=p/q-3

$$2 \sqrt { 5 } = \frac { p } { q } - 3$$

Solve for q

$$q=-\frac{\left(3-2\sqrt{5}\right)p}{11}$$

$$p\neq 0$$

Steps for Solving Linear Equation

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

$$2\sqrt{5}q=p+q\left(-3\right)$$

Subtract q\left(-3\right) from both sides.

$$2\sqrt{5}q-q\left(-3\right)=p$$

Multiply -1 and -3 to get 3.

$$2\sqrt{5}q+3q=p$$

Combine all terms containing q.

$$\left(2\sqrt{5}+3\right)q=p$$

Divide both sides by 2\sqrt{5}+3.

$$\frac{\left(2\sqrt{5}+3\right)q}{2\sqrt{5}+3}=\frac{p}{2\sqrt{5}+3}$$

Dividing by 2\sqrt{5}+3 undoes the multiplication by 2\sqrt{5}+3.

$$q=\frac{p}{2\sqrt{5}+3}$$

Divide p by 2\sqrt{5}+3.

$$q=\frac{\left(2\sqrt{5}-3\right)p}{11}$$

Variable q cannot be equal to 0.

$$q=\frac{\left(2\sqrt{5}-3\right)p}{11}\text{, }q\neq 0$$

Solve for p

$$p=\left(2\sqrt{5}+3\right)q$$

$$q\neq 0$$