Question 46979
{{{(k)/(7-k)-(2)/(k)=3}}}[Find the lowest common denominator (LCD) = (7-k)(k)]
{{{(k)(7-k)(k)/(7-k)-(2)(7-k)(k)/(k)=3(7-k)(k))}}}[Multiply terms by the LCD]
{{{((k)(k))-((2)(7-k))=3(7-k)(k)))}}} [Cancel out]
{{{((k^2))-((14-2k))=((21k-3k^2))))}}}[Multiply]
{{{((k^2))-((14-2k))=((21k-3k^2))))}}}[Subtract the left side]
{{{((k^2+3k^2)-14+2k-21k)}}}
{{{((4k^2-14-19k))))}}} [Combine like-terms]
{{{((4k^2-19k-14))))}}} [Rearrange the terms]

.

{{{x=(--19 +- sqrt( (-19^2)-(4)(4)(-14) ))/((2)(4))}}} [Plug into the quadratic formula]
{{{x=(19 +- sqrt( (585) ))/((8))}}} [Plug into the quadratic formula]
{{{x=(19 +- sqrt( (9)(65) ))/((8))}}}
{{{x=(19 +- 3sqrt((65) ))/((8))}}} 
x=5.398
x=-0.6483