Пусть x = z + 5/2
Тогда
(x – 1)(x – 2)(x – 3)(x – 4) = (z + 3/2)(z + ½)(z – ½)(z – 3/2) =
= (z² – (3/2)²)(z² – (½)²) = (z² – 9/4)(z² – ¼) = (z²)² – 5/2·z² + 9/16 = 15
(z²)² – 5/2·z² + 25/16 = 15 + 25/16 – 9/16
(z² – 5/4)² = 16 = 4²
(z² – 5/4)² – 4² = 0
(z² – 5/4 – 4)(z² – 5/4 + 4) = (z² – 21/4)(z² + 11/4) = 0
z² + 11/4 > 0
z² – 21/4 = 0 при z = ±√21/2; x = (5 ± √21)/2
Ответ: x = (5 ± √21)/2