SOLUTION: how do I solve for x in 6x^2-x^3=64/3

The only feasible way to solve it is
by using your TI-83 or 84

Press CLEAR
Press Y=
Beside \Y1= type the left side 6X^2-X^3
Beside \Y2= type the right side 64/3
Press WINDOW
 
Set window to

Xmin=-10
Xmax=10
Xscl=1
Ymin=-80
Ymax=100
Yscl=10
Xres=1

Press GRAPH
Press 2nd
Press TRACE
Press 5
Press ENTER
Press ENTER
Press ENTER

You see a graph and at the bottom of the screen you see:

Intersection
X=2.4521474 Y=21.333333

That means one solution is X=2.452147474

Press 2nd
Press TRACE
Press 5
Press the left arrow 18 times
Press ENTER
Press ENTER
Press ENTER

You see:

Intersection
X=-1.667973  Y=21.333333

That means another solution is X=-1.667973

Press 2nd
Press TRACE
Press 5
Press the left arrow 30 times
Press ENTER
Press ENTER
Press ENTER

You see:

Intersection
X=5.2158258  Y=21.333333

That means the third and final solution is X=5.2158258

Edwin