First, add 5n^2 to both sides of the equation. This results in
n^2 + 6n + 16 = 0
You may now solve this for n using one of the following approaches:
1) completing the square
2) quadratic formula
3) factoring
4) graphing
Let's compare n^2 + 6n + 16 = 0 to ax^2 + bx + c = 0. see that a=1, b=6 and c=16?
-(6) plus or minus sqrt(6^2 - 4(1)(16)
Then n = --------------------------------------------------
2
Notice that the discriminant, 6^2 - 4(1)(16) is negative: 36-64 = -28
Thus, the two roots of this quadratic are complex: they have real and imaginary parts both.
-6 plus or minus sqrt (-28)
n = -------------------------------------
2
sqrt(-28) comes out as i sqrt(4)sqrt(7), or i2sqrt(7).
Thus, the roots are
-6 plus or minus 2isqrt(7)
n = --------------------------------------
2
One is -3 + sqrt(7); the other is -3 - sqrt(7).
