Verified answer

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

Решим по отдельности:

[tex] {2x}^{2} + 5x - 3 > 0 \\ D = {5}^{2} - 4 \times 2 \times ( - 3) = 25 + 24 = 49 \\ x1x2 = \frac{ - 5± \sqrt{49} }{2 \times 2} = \frac{ - 5±7}{4} \\ x1x2 = - 3 \: ; \: 0.5[/tex]

[tex] {2x}^{2} - 5x + 2 > 0 \\ D = {( - 5)}^{2} - 4 \times 2 \times 2 = 25 - 16 = 9 \\ x1x2 = \frac{ - ( - 5)± \sqrt{9} }{2 \times 2} = \frac{5±3}{4} \\ x1x2 = 0.5 \: ; \: 2[/tex]