Answer
all the real numbers
Work Step by Step
$2(2x^2-3x)>-9$, hence $4x^2-6x+9\gt 0.$ If I complete the square and divide by $6.75$, then $\frac{16}{27}\cdot(x-0.75)^2>-1$. The square of all real numbers is non-negative, hence the square of all real numbers multiplied by a positive constant is non-negative, hence the solution set is all the real numbers. (also, see the graph of $\frac{16}{27}\cdot(x-0.75)^2$
