We can use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
to solve an equation in the form ax² + bx + c = 0.
So, let's first rewrite the given equation as:
9x² - 6x = 11
9x² - 6x - 11 = 0
Now, we can see that:
a = 9
b = -6
c = -11
Then, using those values in the quadratic formula, we obtain:
[tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot9\cdot(-11)}}{2\cdot9} \\ \\ x=\frac{6\pm\sqrt[]{36+36\cdot11}}{18} \\ \\ x=\frac{6\pm\sqrt[]{36(1+11)}}{18} \\ \\ x=\frac{6\pm6\sqrt[]{12}}{18} \\ \\ x=\frac{6(1\pm\sqrt[]{4\cdot3})}{6\cdot3} \\ \\ x=\frac{1\pm2\sqrt[]{3}}{3} \end{gathered}[/tex]
Therefore, option D is correct.
