To solve the inequality, we first simplify the expression on the left side:

Хsqrt(5) + 16x + 9sqrt(5) < 12
=> (Х + 9)sqrt(5) + 16x < 12
=> sqrt(5)(Х + 9) + 16*x < 12

Next, we can isolate the x term by subtracting sqrt(5)*(Х + 9) from both sides:

16x < 12 - sqrt(5)(Х + 9)
=> 16x < 12 - sqrt(5)Х - 9sqrt(5)
=> 16x + sqrt(5)Х < 12 - 9sqrt(5)

Finally, we can divide by (16+sqrt(5)) to isolate x:

x < (12 - 9*sqrt(5))/(16 + sqrt(5))

Therefore, the solution for the inequality Хsqrt(5)+16x+9sqrt(5) < 12 is x < (12 - 9sqrt(5))/(16 + sqrt(5)).