-5x2<45

To solve the inequality \(-5x^2 < 45\), we first rearrange it:

1. Divide both sides by \(-5\). Remember that dividing by a negative number reverses the inequality sign:

   \[ x^2 > -\frac{45}{5} \]

   which simplifies to:

   \[ x^2 > -9 \]

2. Since \(x^2\) (the square of a real number) is always greater than or equal to zero, this inequality \(x^2 > -9\) will always be true for all real \(x\).

Thus, the solution set is:

\[ \text{All real numbers} \quad (-\infty, \infty) \]

This means any real number \(x\) satisfies the inequality.