Step-by-step Solution:

Given equation: \[ x^2 + 2ax + 10 - 3a > 0 \] According to the given condition, we have: \[ 4a^2 - 4(10 - 3a) < 0 \] \[ \Rightarrow a^2 + 3a - 10 < 0 \] \[ \Rightarrow (a + 5)(a - 2) < 0 \] \[ \Rightarrow -5 < a < 2 \]