Question

How do you solve `1/2 - 3/2x = 4/x - 5/12`?

Answer 1

The equation doesn't have a real solution

Explanation:

Multiply both sides by `12x` (which is the LCM of 2, 12 and x)

`6x - 18x^2 = 48 - 5x`

Make one of the sides equal zero,

`-18x^2 + 11x - 48 = 0`
`18x^2 - 11x + 48 = 0`

Use the quadratic formula

`x = (11 +- sqrt(121 -4*18*48))/36 = (11 +- sqrt(-3335))/36`

So the equation doesn't have a real solution. We could expand that root using complex numbers if you want but for Algebra just stopping here should do.