$$x^2-\left(3-2\sqrt{2}\right)x+4-3\sqrt{2 }=0$$

$$a=1 , b=-\left(3-2\sqrt{2}\right) , c=4-3\sqrt{2}$$

$$x_{1,2}=\frac{-\left(-\left(3-\sqrt{2}\right)\right)\pm \sqrt{{\left(-\left(3-2\sqrt{2}\right)\right)}^2-4·1·\left(4-3\sqrt{2}\right)}}{2·1}$$

$$x_{1,2}=\frac{-\left(-3+\sqrt{2}\right)\pm \sqrt{{\left(-3+2\sqrt{2}\right)}^2-4·\left(4-3\sqrt{2}\right)}}{2}$$

$$x_{1,2}=\frac{3-\sqrt{2}\pm \sqrt{{\left(-3\right)}^2+2·\left(-3\right)·\left(2\sqrt{2}\right)+{\left(2\sqrt{2}\right)}^2-4·4-4·\left(-3\sqrt{2}\right)}}{2}$$

$$x_{1,2}=\frac{3-2\sqrt{2}\pm \sqrt{9-12\sqrt{2}+4·2-16+12\sqrt{2}}}{2}$$

$$x_{1,2}=\frac{3-2\sqrt{2}\pm \sqrt{9-\cancel{12\sqrt{2}}+8-16+\cancel{12\sqrt{2}}}}{2}$$

$$x_{1,2}=\frac{3-\sqrt{2}\pm \sqrt{1}}{2}$$

$$x_{1,2}=\frac{3-\sqrt{2}\pm 1}{2}$$

$$x_1=\frac{3-\sqrt{2}+1}{2}$$

$$x_1=\frac{4-\sqrt{2}}{2}$$

$$x_1=\frac{4}{2}-\frac{\sqrt{2}}{2}$$

$$x_2=\frac{3-2\sqrt{2}-1}{2}$$

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

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