Question 906528
<pre>
There is a way to make the plotting system handle fraction exponents,
Place the expression in a 2x1 matrix with the blank character "" as the
upper element and the fraction exponent as the lower element.

Don't let u=x. Let {{{matrix(2,1,"",u=x^(7/4))}}} and {{{matrix(2,1,"",u^2=x^(7/2)) }}}. You had that right. 

{{{ matrix(2,1,"",x^(7/2)-6x^(7/4)+9=0) }}}

becomes

{{{u^2-6u+9=0}}}

Then factor:

{{{(u-3)(u-3)=0}}}

And there's just one solution, u=3

Then {{{matrix(2,1,"",u=x^(7/4))}}} becomes

{{{matrix(2,1,"",3=x^(7/4))}}}

Then we raise both sides to the 'reciprocal'th power, 
the {{{4/7}}}ths power


{{{matrix(2,1,"",3^(4/7)=(x^(7/4))^(4/7))}}}

When you multiply those exponents on the right you get


{{{matrix(2,1,"",3^(4/7)=x^1)}}}  

{{{matrix(2,1,"",3^(4/7)=x)}}}

The answer is 'the seventh root of three to the fourth power'.
 
{{{root(7,3^4)}}}{{{""=""}}}{{{root(7,81)}}}or approximately 1.873444005

Edwin</pre>