Problems with pre-calculus

3*sqrt(3*x+1) = 2*sqrt(x-8)  //square each side.

9*(3*x+1) = 4*(x-8)  //Multiply

27x+9 = 4x-32  //subtract 9 from each side

27x = 4x-41  //subtract 4x from each side

27x-4x = -41  //simplify

23x = -41  //divide each side by 23

x = -41/23

 

To prove this, just plug in your x into the original problem.

There are no real solutions. The two curves y = 3sqrt(3x+1) and y = 2sqrt(x-8) do not intersect.

Substituting x = -41/23 as  suggested by the previous answer gets you the square root of a negative quantity.