Is this question impossible? if not with a solution

Yes in its current visual form, this problem is impossible as there isn't enough information. If we know that the two lines are parallel, then we could find x. However, there are no signs that the lines are parallel. What I mean by that, is that there are no parallel line markers. Similarly, there isn't a right angle square marker near the bottom line. Were there any words given to this problem or did it just simply present this diagram with no words?

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Edit: 

Assuming the lines are parallel, then refer to the image attachment for the angle labels

A = 14-4x
B = A = 14-4x
C = 5y-9
D = 8y+42
E = 180 - D = 180 - (8y+42) = -8y+138

B+C = 90
(14-4x)+(5y-9) = 90
-4x+5y+5 = 90
-4x+5y = 85

If the lines are parallel, then 
A = E
14-4x = -8y+138
-4x+8y = 124

The system of equations is
-4x+5y = 85
-4x+8y = 124

Subtract equation 2 from equation 1 to get
-3y = -39
y = 13

Then use that y value to find x
-4x+8y = 124
-4x+8*13 = 124
-4x+104 = 124
-4x+104-104 = 124-104
-4x = 20
x = -5

So the final answer is x = -5

Once again this all depends on if the two lines are parallel.