By splitting the middle term

4x² + 52x - 3 = 0

4x² + (6√ 2x - √2 x) - 3 = 0

4x² + (6√ 2x - √2 x) - 3 = 0

2√2 x (√2x + 3) - (√2x + 3) = 0

(√2x + 3)(2√2 - 1) = 0

⇒ x = -

Verification:

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

α + β = - b/a

() + () = -

=

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

=

- 3/4 = - 3/4