Work Step by Step
The discriminant of the equation = $b^2-4ac=3^2-4(3/2)(6)=-27$ Since the discriminant is negative there are no real zeros of the equation. So, the function never crosses the x-axis. Also, since the coefficient of the first or the leading term is positive, the graph of the equation must then be above the x-axis always. So, the given inequality is satisfied by all real numbers.