Question 891091
Roots, {{{x=(3k+2+- sqrt((3k+2)^2-4*3*18))/(2*3)}}}


Simplify the discriminant, {{{(9k^2-12k+4)-216=9k^2-12k-212}}}


Now you want {{{(3k+2-sqrt(9k^2-12k-212))/6+(3k+2+sqrt(9k^2-12k-212))/6=6}}}


{{{(6k+4+0)/6=6}}}
{{{6k+4=36}}}
{{{3k+2=18}}}
{{{3k=16}}}
{{{highlight(k=16/3)}}}




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Notice, doing much of anything with the discriminant was not needed.