thornluke

1. The problem statement, all variables and given/known data
The equation kx² - 3x + (k+2) = 0 has two distinct real roots. Find the set of possible values of k.


2. Relevant equations
Since the equation has two distinct real roots, b² - 4ac > 0

3. The attempt at a solution
b²-4ac>0
9-4(k+2)(k)>0
9-4(k²+2k) >0
9-4k²-8k>0
= -4k²-8k+9>0
Multiply both sides by -1,
4k²+8k-9>0
(4k-3)(k+3)>0

-3<k<3/4

However the answer is -2.46<k<0.458
I'm lost, help please!