solve the equation
16x^2- 4x^x-1 -12 = 0
I am sure you meant:
16x^2- 4x^(x-1) -12 = 0
Wow, what a nasty equation.
We have no standard way to handle that one.
16x^2 -12 = 4x^(x-1)
by inspection, x = 1 is an obvious solution
Let's see what Wolfram can do with it ....
http://www.wolframalpha.com/input/?i=solve+16x%5E2+-12+%3D+4x%5E(x-1)
looks like x = appr 3.97 is another.