Value of x?

(x^1/4 + 16)^2 = 144 + x^3/2

\((\frac{x^1}{4} + 16)^2 = 144 + \frac{x^3}{2}\\ \frac{1}{16}*(x+ 64)^2 = 144 + \frac{x^3}{2}\\ (x+ 64)^2 = 144*16 + 8x^3\\ x^2+128x+4096=2304+8x^3\\ x^2+96x+1792=8x^3\\ 8x^3-x^2-96x-1792=0\\ \)

Have fun solving that :)

To continue where Melody left off :

8x^3  - x^2  - 96x  - 1792   =  0 

There is only one real solution that occurs at about  x  =6.7755

Here are the real and non-real solutions : http://www.wolframalpha.com/input/?i=8x^3++-x^2++-+96x++-+1792++%3D+0

I've assumed this is meant to be:   (x^(1/4) + 16)^2 = 144 + x^(3/2)

The real number solution is obtained as follows:

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