If the equations $a{x}^2+bx+c=0$ , and $x^3+3x^2+3x+2=0$  have two common roots, then $2a+3b-5$ is

$x^3+3x^2+3x+2=0$ ; 

 $\Rightarrow (x^3-1)+3(x^2+x+1)=0$
$$\begin{gathered} \Rightarrow (x^2+x+1)(x+2)=0; \\ \Rightarrow \text{x=}-\text{2, }\omega ,{\omega }^2 \end{gathered}$$
Common roots $\omega ,{\omega }^2$ 

 $\therefore \omega ,{\omega }^2$ are common roots of two equation  $\therefore a=b=c=1$