By splitting the middle term

y² + y - 5 = 0

2y² + 3√5y - 10 = 0

2y² + (4√5y - √5y) - 10 = 0

2y² + (4√5y - √5y) - 10 = 0

2y(y + 2√5) - √5(y + 2√5) = 0

(y + 2√5)(2y - √5) = 0

⇒ y = - 2√5, √5/2

Verification:

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

α + β = - b/a

(- 2√5) + (√5/2) = - (3√5)/2

= - 3√5/2 = - 3√5/2

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

(- 2√5)(√5/2) = - 5

- 5 = - 5