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w^2=8w-12


w^2-8w+12=0


w -6


w -2


(w-6)(w-2)=0


w=6


w=2

Answer:  

w=2 , w=6 are the zeroes of the expression

Explanation:

We have been given the expression [tex]\frac{w}{2w-3}=\frac{4}{w}[/tex]

after cross multiplication of the given expression so as to simplify it we will get [tex]\Rightarrow w^2=4(2w-3)\\\\\Rightarrow w^2=8w-12\\\\\Rightarrow w^2-8w+12=0\\\\\Rightarrow w^2-6w-2w+12\\\\(w-2)(w-6)=0\\\\w=2,6[/tex]

Solution to the given equation is w=2,w=6

Therefore these are the solutions of the given expression.