Question 3243
The first thing you want to do is make this formula look nice. Take {{{3 - (4/x) - (2/x^2) = 0}}} and multiply both sides by {{{x^2}}}. This will give you:<br>
{{{3x^2 - 4x - 2 = 0}}}.<br>
This is a lot easier to look at, but keep in mind, x = 0 could be a problem.<br>
To find the roots of this equation, use the quadratic formula:<br>
{{{(-b +- sqrt(b^2 - 4ac))/(2a)}}}.<br>
Setting a = 3, b = -4 and c = -2, the quadratic formulat becomes:<br>
{{{(4 +- sqrt((-4)^2 - 4(3)(-2)))/(2(3)) = (4 +- sqrt(16 + 24))/6 = (4 +- sqrt(40))/6}}}.<br>
So the roots of the equation are {{{(4 + sqrt(40))/6}}} and {{{(4 - sqrt(40))/6}}}. If you plug these numbers into a calculator you will see they work.