Question

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

Answer 1

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

Explanation:

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`

Do the quadratic formula:

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

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

Solve for x:

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