Question

How do you solve `3/6x + 1/2 = 8/x + 4/3`?

Answer 1

Solution is `(5+-sqrt601)/6`

Explanation:

The equation `3/6x+1/2=8/x+4/3` is valid only if `x!=0`. Hence multiplying each term by `6x` we get

`3x^2+3x=48+8x`, which simplifies to

`3x^2-5x-48=0`

The solution of general form of quadratic equation `ax^2+bx+c=0` is `(-b+-sqrt(b^2-4ac))/(2a)` and here as `a=3, b=-5, c=-48`, soltion is given by

`(-(-5)+-sqrt((-5)^2-4*3*(-48)))/(2*3)` or

`(5+-sqrt(25+576))/6` or `(5+-sqrt601)/6`