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Assuming it is just the x under the square root sign, here is a graphical/numerical approach:

So the solutions are 0.125, 3.209 and 31.875 (to 3dp).

Is it just the x that is under the square root?

(x-5√x +1)(x-4) =6(√x -1)^2

Solve for x:
(x-4) (1-5 sqrt(x)+x) = 6 (sqrt(x)-1)^2

Subtract 6 (sqrt(x)-1)^2 from both sides:
(x-4) (1-5 sqrt(x)+x)-6 (sqrt(x)-1)^2 = 0

(x-4) (1-5 sqrt(x)+x)-6 (sqrt(x)-1)^2  =  -10+32 sqrt(x)-9 x-5 x^(3/2)+x^2:
-10+32 sqrt(x)-9 x-5 x^(3/2)+x^2 = 0

Simplify and substitute y = sqrt(x):
 -10+32 sqrt(x)-9 x-5 x^(3/2)+x^2  =  -10+32 sqrt(x)-9 sqrt(x)^2-5 sqrt(x)^3+sqrt(x)^4  =  y^4-5 y^3-9 y^2+32 y-10  =  0:
y^4-5 y^3-9 y^2+32 y-10 = 0

The left hand side factors into a product with two terms:
(y^2-6 y+2) (y^2+y-5) = 0

Split into two equations:
y^2-6 y+2 = 0 or y^2+y-5 = 0

Subtract 2 from both sides:
y^2-6 y = -2 or y^2+y-5 = 0

Add 9 to both sides:
y^2-6 y+9 = 7 or y^2+y-5 = 0

Write the left hand side as a square:
(y-3)^2 = 7 or y^2+y-5 = 0

Take the square root of both sides:
y-3 = sqrt(7) or y-3 = -sqrt(7) or y^2+y-5 = 0

Add 3 to both sides:
y = 3+sqrt(7) or y-3 = -sqrt(7) or y^2+y-5 = 0

Substitute back for y = sqrt(x):
sqrt(x) = 3+sqrt(7) or y-3 = -sqrt(7) or y^2+y-5 = 0

Raise both sides to the power of two:
x = (3+sqrt(7))^2 or y-3 = -sqrt(7) or y^2+y-5 = 0

Add 3 to both sides:
x = (3+sqrt(7))^2 or y = 3-sqrt(7) or y^2+y-5 = 0

Substitute back for y = sqrt(x):
x = (3+sqrt(7))^2 or sqrt(x) = 3-sqrt(7) or y^2+y-5 = 0

Raise both sides to the power of two:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or y^2+y-5 = 0

Add 5 to both sides:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or y^2+y = 5

Add 1/4 to both sides:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or y^2+y+1/4 = 21/4

Write the left hand side as a square:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or (y+1/2)^2 = 21/4

Take the square root of both sides:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or y+1/2 = sqrt(21)/2 or y+1/2 = -sqrt(21)/2

Subtract 1/2 from both sides:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or y = sqrt(21)/2-1/2 or y+1/2 = -sqrt(21)/2

Substitute back for y = sqrt(x):
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or sqrt(x) = sqrt(21)/2-1/2 or y+1/2 = -sqrt(21)/2

Raise both sides to the power of two:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or x = (sqrt(21)/2-1/2)^2 or y+1/2 = -sqrt(21)/2

Subtract 1/2 from both sides:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or x = (sqrt(21)/2-1/2)^2 or y = -1/2-sqrt(21)/2

Substitute back for y = sqrt(x):
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or x = (sqrt(21)/2-1/2)^2 or sqrt(x) = -1/2-sqrt(21)/2

Raise both sides to the power of two:
x = (3+sqrt(7))^2 or x = (3-sqrt(7))^2 or x = (sqrt(21)/2-1/2)^2 or x = (-1/2-sqrt(21)/2)^2

(x-4) (1-5 sqrt(x)+x) => ((3-sqrt(7))^2-4) (1-5 sqrt((3-sqrt(7))^2)+(3-sqrt(7))^2)  =  66-24 sqrt(7) ~~ 2.50197
6 (sqrt(x)-1)^2 => 6 (sqrt((3-sqrt(7))^2)-1)^2  =  66-24 sqrt(7) ~~ 2.50197:
So this solution is correct

(x-4) (1-5 sqrt(x)+x) => ((3+sqrt(7))^2-4) (1-5 sqrt((3+sqrt(7))^2)+(3+sqrt(7))^2)  =  66+24 sqrt(7) ~~ 129.498
6 (sqrt(x)-1)^2 => 6 (sqrt((3+sqrt(7))^2)-1)^2  =  6 (2+sqrt(7))^2 ~~ 129.498:
So this solution is correct

(x-4) (1-5 sqrt(x)+x) ~~ -19.5826
6 (sqrt(x)-1)^2 => 6 (sqrt((-1/2-sqrt(21)/2)^2)-1)^2  =  33-3 sqrt(21) ~~ 19.2523:
So this solution is incorrect

(x-4) (1-5 sqrt(x)+x) ~~ 3.75682
6 (sqrt(x)-1)^2 => 6 (sqrt((sqrt(21)/2-1/2)^2)-1)^2  =  -9 (sqrt(21)-5) ~~ 3.75682:
So this solution is correct

The solutions are:
Answer: |  x = (3+sqrt(7))^2             or x = (3-sqrt(7))^2                 or x = (sqrt(21)/2-1/2)^2