Question

Solve for n. M=n-2/n

Answer 1

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

`n=(-b+/-√(b^2-4ac))/(2a)`

in this case
0=1n²-1n-2-M
a=1
b=-1
c=(-2-M)
so


`n=(-(-1)+/-√((-1)^2-4(1)(-2-M)))/(2(1))`

`n=(1+/-√(1+8+4M))/(2)`

`n=(1+/-√(9+4M))/(2)`

so

`n=(1+√(9+4M))/(2)` and
`n=(1-√(9+4M))/(2)`