f(x) = 0, where

f(x) = -5x2 + 8x + 9

just use your normal methods to solve quadratic equations:

-5x^2+8x+9 = 0

I don't see any easy way to factor that, so try the quadratic formula or completing the square.

In google type :

quadratic equation online

When you see list of results click on:

Free Online Quadratic Equation Solver: Solve by Quadratic...

When page be open in rectanlgle type:

-5 x ^ 2 + 8x + 9 = 0

and click option :

solve it!

You will see solution step - by - tep

To find the value of x when f(x) = 0, we need to solve the equation -5x^2 + 8x + 9 = 0.

This is a quadratic equation, so we can use the quadratic formula to solve for x. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Applying this formula to our equation, we have:
a = -5, b = 8, c = 9

Plugging in the values, we get:
x = (-8 ± √(8^2 - 4(-5)(9))) / (2(-5))

Simplifying further:
x = (-8 ± √(64 + 180)) / (-10)
x = (-8 ± √244) / (-10)
x = (-8 ± 2√61) / (-10)

So the solutions for x are x = (-8 + 2√61) / (-10) and x = (-8 - 2√61) / (-10).

Now, you can calculate the values of x using a calculator or simplify further if necessary.