Question 31462
First, you need to put the equation in standard form:

{{{4n^2 = -6n - 1}}}


{{{4n^2 + 6n + 1 = 0}}}


Now, you can use the quadratic formula to solve this.  

{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


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


{{{n = (-6 +- sqrt( 36-16 ))/8 }}}


{{{n = (-6 +- sqrt( 20 ))/8 }}}




Now, to look at your two solutions:


{{{n[1] = (-6 + sqrt( 20 ))/8 }}}

{{{n[1] = -0.19098300562505257589770658281718}}}


{{{n[2] = (-6 - sqrt( 20 ))/8 }}}

{{{n[2] = -1.3090169943749474241022934171828}}}