Solve the Quadratic Equation by Factorization: 6x − 10/x = 27

Question: Solve the following quadratic equation by factorization:

$$ 6x-\frac{10}{x}=27 $$

Solution

$$ 6x^2-10=27x $$

$$ 6x^2-27x-10=0 $$

$$ 6x^2-30x+3x-10=0 $$

$$ 6x(x-5)+2(x-5)=0 $$

$$ (2x+1)(3x-10)=0 $$

Either

$$ 2x+1=0 $$

$$ x=-\frac{1}{2} $$

$$ 3x-10=0 $$

$$ x=\frac{10}{3} $$

Hence,

$$ \boxed{x=-\frac{1}{2},\ \frac{10}{3}} $$

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