Is there non real number of x that sufficient for this $11-\sqrt 7 x = 4x - 10$ 
Is there non real number of x that sufficient for $11-\sqrt 7 x = 4x - 10$ and $|\sqrt 7 x - 11 | = 4x - 10$

There is a solution which is real number.

The only solution to $11-\sqrt 7 x = 4x - 10$ is $x=\dfrac{21}{4+\sqrt{7}}$.  
It is a real number, about $3.16$
It also satisfies $|\sqrt 7 x - 11 | = 4x - 10$
