Question 98447
Given equation 

6n^2= -8n-1 

add 8n +1 on both sides

6n^2 + 8n + 1 =0  ( looks more familiar now ?)
use the quadratic formula 
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{n= (-8 +- sqrt(8^2 - 4*6*1))/(2*6)}}}
{{{n= (-8 +- sqrt(64 - 24))/12}}}
{{{n= (-8 +- sqrt(40))/12}}}
{{{n= (-8 +- 6.325 )/12)}}}
n= -1.193 and n= -0.1396