Find $\tan x $ if $\sin x+\cos x=\frac12$ It is given that $0 < x < 180^\circ$ and $\sin x+\cos x=\frac12$, Find $\tan x $. 
I tried all identities I know but I have no idea how to proceed.  Any help would be appreciated. 

Hint :
\begin{align}
\sin x+\cos x&=\frac12\\
\sin x&=\frac12-\cos x\\
\sin^2 x&=\left(\frac12-\cos x\right)^2\\
1-\cos^2 x&=\frac14-\cos x+\cos^2 x\\
2\cos^2 x-\cos x-\frac34&=0\\
8\cos^2 x-4\cos x-3&=0
\end{align}
