Step-by-step explanation:
[tex] => 2 {x}^{2} + \frac{7}{2}x + \frac{3}{4} = 0[/tex]
[tex] => \frac{8 {x}^{2} + 14x + 3}{4} = 0 [/tex]
[tex] => 8 {x}^{2} + 14x + 3 = 0[/tex]
[tex] => 8 {x}^{2} + 12x + 2x + 3 = 0[/tex]
[tex] => 4x(2x + 3) + 1(2x + 3) = 0[/tex]
[tex] = > (2x + 3)(4x + 1) = 0[/tex]
[tex] = > x = - \frac{3}{2} or \frac{ - 1}{4} [/tex]
option C
