Question 196022
Let the smaller even integer be {{{n}}}
The next larger even integer will be {{{n + 2}}}
given:
{{{n*(n + 2) = 9n + 30}}}
------------------------
{{{n^2 + 2n = 9n + 30}}}
{{{n^2 - 7n - 30 = 0}}}
Using quadratic formula:
{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = -7}}}
{{{c = -30}}}
{{{n = (-(-7) +- sqrt( (-7)^2-4*1*(-30) ))/(2*1) }}}
{{{n = (7 +- sqrt( 49 + 120 )) / 2 }}}
{{{n = (7 +- 13) / 2 }}} (I'll ignore the negative root)
{{{n = 20/2}}}
{{{n = 10}}}
{{{n + 2 = 12}}}
The integers are 10 and 12
check:
{{{n*(n + 2) = 9n + 30}}}
{{{10*12 = 9*10 + 30}}}
{{{120 = 90 + 30}}}
{{{120 = 120}}}
OK