5х^4-3^2-5=0

To solve the equation \( 5x^4 - 3^2 - 5 = 0 \), we can first simplify the equation.

First, calculate \( 3^2 \):

\[ 3^2 = 9 \]

Now, substitute that back into the equation:

\[ 5x^4 - 9 - 5 = 0 \]

Combine like terms:

\[ 5x^4 - 14 = 0 \]

Now, add 14 to both sides of the equation:

\[ 5x^4 = 14 \]

Next, divide both sides by 5:

\[ x^4 = \frac{14}{5} \]

Now, take the fourth root of both sides:

\[ x = \pm \sqrt[4]{\frac{14}{5}} \]

This can also be simplified as:

\[ x = \pm \frac{\sqrt[4]{14}}{\sqrt[4]{5}} \]

So, the solutions to the equation \( 5x^4 - 3^2 - 5 = 0 \) are:

\[ x = \frac{\sqrt[4]{14}}{\sqrt[4]{5}} \quad \text{and} \quad x = -\frac{\sqrt[4]{14}}{\sqrt[4]{5}} \]