Question 1001818
n and n+1 are the numbers.


{{{1/n+1/(n+1)=7/12}}}


n and n+1 are the numbers.


{{{1/n+1/(n+1)=7/12}}}
LCD is 12n(n+1), so multiply both sides by LCD.
{{{12(n+1)+12n=7n(n+1)}}}
{{{12n+12+12n=7n&2+7n}}}
{{{24n+12=7n^2+7n}}}
{{{7n^2-17n-12=0}}}


{{{n=(17+- sqrt(17^2+4*7*12))/14}}}
{{{n=(17+- sqrt(625))/14}}}
{{{highlight_green(highlight(n=(17+- 25)/14))}}}


Either {{{n=-8/14}}}  OR  {{{n=3}}}.
Obviously the acceptable value must be {{{highlight(n=3)}}} for the first consecutive number, IF the numbers must be integers..


The numbers are 3 and 4
(For integer results)