By splitting the middle term

2x² + 7x/2 + 3/4 = 0

8x² + 14x + 3 = 0

8x² + (12x + 2x) + 3 = 0

8x² + 12x + 2x + 3 = 0

4x (2x + 3) + (2x + 3) = 0

(2x + 3)(4x + 1) = 0

⇒ x = - 3/2, - 1/4

Verification:

Sum of the zeroes = - (coefficient of x) ÷ coefficient of x²

α + β = - b/a

(- 3/2) + (- 1/4) = - (7)/4

= - 7/4 = - 7/4

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

(- 3/2)(- 1/4) =

3/8 = 3/8