multiply both sides by n
nM=n²-2
minus n both sides
M=n²-n-2
minus M both sides
0=n²-n-2-M
use quadratic formual
for 0=an²+bn+c
[tex]n=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
in this case
0=1n²-1n-2-M
a=1
b=-1
c=(-2-M)
so
[tex]n=\frac{-(-1)+/-\sqrt{(-1)^2-4(1)(-2-M)}}{2(1)}[/tex]
[tex]n=\frac{1+/-\sqrt{1+8+4M}}{2}[/tex]
[tex]n=\frac{1+/-\sqrt{9+4M}}{2}[/tex]
so
[tex]n=\frac{1+\sqrt{9+4M}}{2}[/tex] and [tex]n=\frac{1-\sqrt{9+4M}}{2}[/tex]
