$${\left(x+4\right)}^2+\left(x+1\right)\left(x+2\right)=9$$

$$\left(x^2+2·x·4+4^2\right)+\left(x^2+2x+x+2\right)=9$$

$$\left(x^2+8x+16\right)+\left(x^2+3x+2\right)=9$$

$$2x^2+11x+18=9$$

$$2x^2+11x+9=0$$

$$a=2 ; b=11 ; c=9$$

$$x_{1,2}=\frac{-11\pm \sqrt{{11}^2-4·2·9}}{2·2}$$

$$x_{1,2}=\frac{-11\pm \sqrt{121-72}}{4}$$

$$x_{1,2}=\frac{-11\pm \sqrt{49}}{4}$$

$$x_{1,2}=\frac{-11\pm 7}{4}$$

$$x_{1,2}=\frac{-11+7}{4}$$

$$x_1=-\frac{4}{4}$$

$$x_1=-1$$

$$x_2=\frac{-11-7}{4}$$

$$x_2=-\frac{18}{4}$$

$$x_2=-\frac{9}{2}$$