In order to find the possible values of k, first let's put the equation in the standard form and equate it to zero:

So we have:

Now, let's calculate the discriminant:

In order to have real roots, the value of the discriminant must be greater than zero, so we have:
![\begin{gathered} \Delta>0 \\ 16k^2+52k+40>0 \\ 4k^2+13k+10>0 \\ k=\frac{-13\pm\sqrt[]{13^2-4\cdot4\cdot10}}{2\cdot4} \\ k=\frac{-13\pm\sqrt[]{169-160}}{8} \\ k_1=(-13+3)/(8)=-(10)/(8)=-1.25 \\ k_2=(-13-3)/(8)=-2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/vymtu3mrirfu5kmr6hod772i0cyohkpc5t.png)
Since the coefficient of k² is positive, the discriminant will be positive for k < k2 or k > k1, that is:
