Find the set of values of k for which this equation has two real roots.
5x^2 + 4k*x + k = x^2 + 3x + 2
+128448 Rearrange as
4x^2 + (4k - 3)x + k - 2 = 0
This will have two real roots when the discriminant > 0
So
(4k - 3)^2 - 4 (4) (k - 2) > 0
16k^2 - 24k + 9 - 16k + 32 > 0
16k^2 - 40k + 41 > 0
See the graph here (in x) : https://www.desmos.com/calculator/bwva5lob60
This parabola lies wholly above the x axis so any real value of k will give two real solutions
