Question 291619
Let {{{n}}} = the unknown number
given:
{{{6n + 2*(1/n) = 13}}}
Multiply both sides by {{{n}}}
{{{6n^2 + 2 = 13n}}}
{{{6n^2 - 13n + 2 = 0}}}
Solve using quadratic formula
{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 6}}}
{{{b = -13}}}
{{{c = 2}}}
{{{n = (-(-13) +- sqrt( (-13)^2-4*6*2 ))/(2*6) }}}
{{{n = (13 +- sqrt(169 - 48 ))/12 }}}
{{{n = (13 +- sqrt(121 ))/12 }}}
{{{n = (13 +- 11)/12}}}
The solutions are:
{{{n = (13 + 11)/12}}}
{{{n = 2}}}
and
{{{n = (13 - 11)/12}}}
{{{n = 1/6}}}
Both these solutions work if you plug them
back into {{{6n + 2*(1/n) = 13}}}