Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.
Simplify as
x^2 + (17 - m)x + 4 = 0
If we have two distinct roots then the discriminant is > 0
So
(17- m)^2 - 4*4 > 0
(17 - m)^2 > 16 take both roots
17 - m > 4 17 - m < -4
13 > m 21 < m
m comes from (-inf , 13) U ( 21, inf)
+230 
