What is the solution set for $5/3-2/x=8x$ if $x!=0$ ?

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Answer 1 · 2018-08-07T00:25:12

$x = (5 +- sqrt(551)i)/48$

First, add a 1 as a denominator for 8x:

$5/3 - 2/x = (8x)/1$

Then, find the GCF (Greatest Common Denominator), which in this case is 3x.

$(5x)/(3x) - 6/(3x) = (24x^2)/(3x)$

Next, since there is an equal sign, we can just eliminate the 3x from the denominator and have a simple equation:

$5x - 6 = 24x^2$

Put them all on 1 side.

$24x^2 - 5x + 6 = 0$

$x = -b +- (sqrt(b^2-4ac))/(2a)$

$x = 5 +- (sqrt(25 - 4(24)(6)))/48$

Solve for x:

$x = (5 +- sqrt(551)i)/48$

What is the solution set for 5/3-2/x=8x5/3-2/x=8x if x!=0x!=0?