please help me understand how to do this problem with detail

please help me understand how to do this problem with detailed steps.

Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) (x + 4/x)^2 + 17(x + 4/x) + 72 = 0 x =

Solution

Solution:

Expanding the given equation

we get

(18x²+76x+16)/x² + 72 = 0

90x²+76x+16 = 0

45x² + 38x +8 = 0

on solving this equation , we get

x = -2/5 and -4/9

x = -2/5 ,-4/9

Answer

.