A concave mirror has a focal length of 20cm. Find the positions of an object from pole of mirror for which the image size is double the object size

Let distance of object from mirror is x
$\text{f}=-20\text{\hspace{0.17em}cm}$ 
Image height is double of object height.  The image may be real r virtual 
If image is real 
 $\begin{array}{l}\mathrm{m}=-2\\ \mathrm{m}=-\frac{\mathrm{v}}{\mathrm{u}}\Rightarrow -2=-\frac{\mathrm{v}}{-\mathrm{x}}\Rightarrow \mathrm{v}=-2\mathrm{x}\\ \frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}\Rightarrow \frac{1}{-2\mathrm{x}}+\frac{1}{-\mathrm{x}}=\frac{1}{-20}\Rightarrow \frac{1+2}{2\mathrm{x}}=\frac{1}{20}\\ \mathrm{X}=30\mathrm{cm}\end{array}$
If image is virtual 
$\begin{array}{l}\mathrm{m}=+2\\ \mathrm{m}=-\frac{\mathrm{v}}{\mathrm{u}}\Rightarrow 2=-\frac{\mathrm{v}}{-\mathrm{x}}\Rightarrow \mathrm{v}=2\mathrm{x}\\ \frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}\Rightarrow \frac{1}{2\mathrm{x}}+\frac{1}{-\mathrm{x}}=\frac{1}{-20}\Rightarrow \frac{1-2}{2\mathrm{x}}=\frac{1}{-20}\end{array}$
$\text{x}=10\text{\hspace{0.17em}cm}$