To solve the equation

\[
x^2 - \frac{7}{4} = \frac{9}{4}
\]

we will first isolate \(x^2\). Start by adding \(\frac{7}{4}\) to both sides:

\[
x^2 = \frac{9}{4} + \frac{7}{4}
\]

Now, combine the fractions on the right side:

\[
x^2 = \frac{9 + 7}{4} = \frac{16}{4} = 4
\]

Next, take the square root of both sides:

\[
x = \pm 2
\]

Thus, the solutions to the equation \(x^2 - \frac{7}{4} = \frac{9}{4}\) are:

\[
x = 2 \quad \text{and} \quad x = -2
\]