Question 32574
Solve:
{{{x/2 - 2/3 = 1/x}}} Simplify the left side.
{{{(3x-4)/6 = 1/x}}} Multiply both sides by 6.
{{{3x-4 = 6/x}}} Multiply both sides by x.
{{{3x^2-4x = 6}}} Subtract 6 from both sides.
{{{3x^2-4x-6 = 0}}} Solve this using the quadratic formula:{{{x=(-b+-sqrt(b^2-4ac))/2a}}}.
{{{x = (-(-4)+-sqrt((-4)^2-4(1)(-6)))/2(1)}}}
{{{x = (4+-sqrt(16+24))/2}}}
{{{x = (4+-sqrt(40))/2}}}
{{{x = (4+-2sqrt(10))/2}}}
{{{x = 2+sqrt(10)}}} or {{{x = 2-sqrt(10)}}}