**1. The problem statement, all variables and given/known data**
The equation kx

^{2} - 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, b

^{2} - 4ac > 0

**3. The attempt at a solution**
b

^{2}-4ac>0

9-4(k+2)(k)>0

9-4(k

^{2}+2k) >0

9-4k

^{2}-8k>0

= -4k

^{2}-8k+9>0

Multiply both sides by -1,

4k

^{2}+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!