Question 652142
{{{3n^2=-6n-1}}}

{{{3n^2+6n+1=0}}}...use quadratic formula to solve for {{{n}}}

{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}...note that {{{a=3}}}, {{{b=6}}} and {{{c=1}}}


{{{n = (-6 +- sqrt( 6^2-4*3*1 ))/(2*3) }}}

{{{n = (-6 +- sqrt(36-12 ))/6 }}}

{{{n = (-6 +- sqrt(24 ))/6 }}}


{{{n = (-6 +- 4.898979)/6 }}}

solutions:

{{{n = (-6 + 4.898979)/6 }}}

{{{n = -1.101021/6 }}}

{{{highlight(n = -0.1835035) }}}

or

{{{n = (-6 - 4.898979)/6 }}}

{{{n = -10.898979/6 }}}

{{{highlight(n = -1.8164965) }}}