Question 664042
First get the equation into standard form 


{{{8n^2-4n=18}}}


{{{8n^2-4n-18=18-18}}}


{{{8n^2-4n-18=0}}}


Now use the quadratic formula to solve for n


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


{{{n = (-(-4)+-sqrt((-4)^2-4(8)(-18)))/(2(8))}}}


{{{n = (4+-sqrt(16-(-576)))/(16)}}}


{{{n = (4+-sqrt(16+576))/(16)}}}


{{{n = (4+-sqrt(592))/16}}}


{{{n = (4+sqrt(592))/16}}} or {{{n = (4-sqrt(592))/16}}}


{{{n = (4+4*sqrt(37))/16}}} or {{{n = (4-4*sqrt(37))/16}}}


{{{n = (1+sqrt(37))/4}}} or {{{n = (1-sqrt(37))/4}}}


{{{n = 1.77069}}} or {{{n = -1.27069}}}


So the exact solutions are {{{n = (1+sqrt(37))/4}}} or {{{n = (1-sqrt(37))/4}}}


and the approximate solutions are {{{n = 1.77069}}} or {{{n = -1.27069}}}