Finding a maximum X value for equation.

Im having a hard time finding a maximum value. Well, i can find it, but its not the correct value.

Here is the problem:

A rectangular piece of cardboard measuring 26 inches by 47 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let X represent the length of each side of each such square. For what value of X will the volume be a maximum ?

So Im thinking the equation is set up like this:

(26-2x)(47-2x)(x)=V

And after foiled out:

x(4x^2-146x+1222)

and then I apply vertex formula to get the x value: -b/2a= 146/8= 18.25

Wouldnt 18.25 be the x value? Its says the correct answer is 5.37. What am I doing wrong?