Question 117222
{{{n/(n-4)+n=12-4n/(n-4)}}}………multiply both sides by {{{n-4}}}

{{{(n(n-4)/(n-4)) +n (n-4) =12(n-4) - 4n(n-4)/(n-4)}}}………simplify, and multiply

{{{n(cross(n-4))/(cross(n-4)) +n (n-4) =12(n-4) - 4n(cross(n-4))/(cross(n-4))}}}………


{{{n+n^2-4n = 12n-48-4n}}}………


{{{n^2-11n+48= 0}}}………




the roots are:


{{{n[1,2]=(-b +- sqrt (b^2 -4*a*c )) / (2*a)}}}
	
{{{n[1,2]=(-(-11) +- sqrt ((-11)^2 -4*1*48 )) / (2*1)}}}

{{{n[1,2]=(11 +- sqrt (121 - 192 )) / 2}}}

{{{n[1,2]=(11 +- sqrt (-71 )) / 2}}}

{{{n[1,2]=(11 +- sqrt (71(-1) )) / 2}}}

{{{n[1,2]=(11 +- 8.4i ) / 2}}}
	
	
{{{n[1]=(11 + 8.4i ) / 2}}}

{{{n[1]= 5.5 + 4.2i}}}


{{{n[2]=(11 - 8.4i ) / 2}}}

{{{n[2]= 5.5 - 4.2i}}}