Move, the (x-l) in the denominator to the numerator on the other side of the equal sign. Then distribute the factors with x in them. Post back with your work so we can offer additional help.
Since the big expression [MATH]\frac{z\sqrt{np(1-p)}}{n}[/MATH] is effectively a constant, you may find the work easier if you temporarily replace it with a single variable: [MATH]A=\frac{-lp-x(1-p)}{x-l}[/MATH]. Then do as Jomo suggested.
One way to reduce errors on this kind of problem and “relieve the imagination” is called “substitution of variables.
Turn complex factors of x into single variables.
[MATH]\text {Let } u = (1 - p) \text { and } v = \sqrt{np(1 - p)}.[/MATH]
[MATH]\therefore z = \dfrac{- \{Lp + x(1 - p)\}n}{(x - L)\sqrt{np(1 - p)}} = \dfrac{- n(Lp + xu)}{v(x - L)}.[/MATH]
Easier to understand and far less likely to make a transcription error. Now clear fractions as jomo suggested.
[MATH]x = L * \dfrac{z\sqrt{np(1 - p)} - np}{z \sqrt{np(1 - p)} + n(1 - p)}.[/MATH]
That is equivalent to what your teacher got but less easy to screw up.
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