What is x if $\frac{2}{x} - 3 x = - 4$ $2/x-3x=-4$ ?

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What is x if $\frac{2}{x} - 3 x = - 4$ $2/x-3x=-4$ ?

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Answer 1 · 2016-03-07T19:51:50

$\frac{2 \pm \sqrt{10}}{3}$ $(2+-sqrt10)/3$

Explanation:

$\frac{2}{x} - 3 x = - 4$ $2/x-3x=-4$
$or 2 - 3 x^{2} = - 4 x$ $or 2-3x^2 = -4x$
$or 3 x^{2} - 4 x - 2 = 0$ $or 3x^2 - 4x - 2 = 0$

which is in the standard quadratic form:
$a x^{2} + b x + c = 0$ $ax^2 + bx + c = 0$

where b = -4, a = 3, c = -2
Hence, the roots of the equation are given by:
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x = (-b +- sqrt(b^2 - 4ac))/(2a)$
$or x = (\frac{4 \pm \sqrt{16 + 24}}{6})$ $or x = ((4 +- sqrt(16+24))/6)$
$or x = \frac{4 \pm \sqrt{40}}{6}$ $or x = (4 +- sqrt 40 )/6$
$or x = \frac{2 \pm \sqrt{10}}{3}$ $or x=(2 +- sqrt10)/3$

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What is x if $\frac{2}{x} - 3 x = - 4$ $2/x-3x=-4$ ?

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Explanation:

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