To solve this quadratic equation, we can use the quadratic formula:

For an equation in the form of [tex]ax^{2} + bx + c = 0[/tex], the solution can be found using the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}[/tex]

In our case, the coefficients are [tex]a = 9[/tex], [tex]b = 6[/tex], and [tex]c = -8[/tex].

Plugging these values into the quadratic formula, we get:

[tex]x = \frac{-6 \pm \sqrt{6^{2} - 4 \cdot 9 \cdot (-8)}}{2 \cdot 9}[/tex]
[tex]x = \frac{-6 \pm \sqrt{36 + 288}}{18}[/tex]
[tex]x = \frac{-6 \pm \sqrt{324}}{18}[/tex]
[tex]x = \frac{-6 \pm 18}{18}[/tex]

Therefore, the solutions to the equation are:

[tex]x = \frac{12}{18} = \frac{2}{3}[/tex]

or

[tex]x = \frac{-24}{18} = \frac{-4}{3}[/tex]