What's the shape of ax^2+bx+c=0 equation?

Note that $ax^2+bx+c=0$ and $y=ax^2+bx+c$ are completely different objects. The former is an equation and the latter is a function. 


The quadratic equation $ax^2+bx+c=0$ has two solutions 
\[x=\frac{-b+\sqrt{b^2-4ac}}{2a},  x=\frac{-b-\sqrt{b^2-4ac}}{2a}  \]
provided $b^2-4ac>0$. Note that these are equations of two veritical lines. If the equation has only one solution ($b^2-4ac=0$), then $ax^2+bx+c=0$ would represent only one straight line. That's why you are getting two straight lines. 

However, if you mean $y=ax^2+bx+c$, then it represents the graph of a parabola.