Question 34497
{{{ 5n^2=-12n-1 }}}
Move all parts to the left side
{{{ 5n^2+12n+1=0 }}}
Use the quadratic equation...
{{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
Substitute
a=5
b=12
c=1
{{{ x = (-12 +- sqrt( 12^2-4*5*1 ))/(2*5) }}}
Work the equation
{{{ x = (-12 +- sqrt( 144-4*5*1 ))/(2*5) }}}
{{{ x = (-12 +- sqrt( 144-20 ))/(2*5) }}}
{{{ x = (-12 +- sqrt( 124 ))/(2*5) }}}
{{{ x = (-12 +- sqrt( 124 ))/(10) }}}
Root out the 124
{{{ x = (-12 +- 2sqrt( 31 ))/(10) }}}
reduce the coefficients
{{{ x = (-6 +- sqrt( 31 ))/(5) }}}
DONE