Question
Solve the following quadratic equation by factorization.
$6 x-\frac{2}{x}=1$
$6 x-\frac{2}{x}=1$
✓
Answer
$\begin{array}{l}6 x^2-2=x \\ \Rightarrow 6 x^2-x-2=0 \\ \Rightarrow 6 x^2+3 x-4 x-2=0 \\ \Rightarrow 3 x(2 x+1)-2(2 x+1)=0 \\ \Rightarrow(3 x-2)(2 x+1)=0 \\ 3 x-2=0 \Rightarrow 3 x=2 \Rightarrow x=\frac{2}{3} \\ 2 x+1=0 \Rightarrow 2 x=-1 \Rightarrow x=-\frac{1}{2}\end{array}$
Hence, ${ }^x=\frac{2}{3}$ and $x=-\frac{1}{2}$ are roots of the equation.
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