Verified answer

Answer:

[tex] {x }^{2} + (2 \sqrt{6} + 5)x + 2 = 0[/tex]

Step-by-step explanation:

[tex] {( \sqrt{3}x + \sqrt{2} ) }^{2} = 2 {x}^{2} - 5x \\ {( \sqrt{3}x) }^{2} + {( \sqrt{2}) }^{2} + 2( \sqrt{3} x)( \sqrt{2} ) = 2 {x}^{2} - 5x \\ 3 {x}^{2} + 2 + 2 \sqrt{6} x = 2 {x}^{2} - 5x \\ 3 {x}^{2} - 2 {x}^{2} + 2 \sqrt{6} x + 5x + 2 = 0 \\ {x}^{2} + (2 \sqrt{6} + 5)x + 2 = 0[/tex]