Help to solve the equation involving complicate fractions

Question

I am trying to solve this equation $${2\over x}-5=5x-{5\over 7}$$

This is what I have tried"

$${2\over x}-5x=5-{5\over 7}$$

$${2-5x^2\over x}={30\over 7}$$

I am not sure how to proceed.

Answer 1

Note that $$\frac{2}{x}-5=5x-\frac{5}{7} \implies 7x\left(\frac{2}{x}-5\right) = 7x\left(5x-\frac{5}{7}\right) \implies35x^2+30x-14=0.$$

Answer 2

See that your question turns to.

$\, \frac{2}{x}-5x = 5-\frac57$

$\implies \, \frac{2-5x^2}{x} =\frac{30}{7}$

$\implies \, 14 - 35x^2 = 30x$

$\implies 35x^2 + 30x - 14 = 0$

Applying the quadratic formula gives you

$x = \frac{- 30 \pm 2\sqrt{715}}{70} $