(a+3)x² + (a + 4)x + 2 = 0
при a = - 3 :
(- 3 + 3)x² + (- 3 + 4)x + 2 = 0
x + 2 = 0
x = - 2 - единственный корень
при a ≠ - 3 :
(a + 3)x² + (a + 4)x + 2 = 0
D = (a+4)² - 4 * (a + 3) * 2 = a² + 8a + 16 - 8a - 24 = a² - 8
D = 0
a² - 8 = 0
a² = 8

Ответ : при a = - 3 ; a = - 2√2 ; 2√2