We have the following:
[tex]10x^2-x+9=0[/tex]solving:
[tex]\begin{gathered} 10x^2-x+9=0 \\ 10x^2-x+9-9=-9 \\ 10x^2-x=-9 \\ \frac{10}{10}x^2-\frac{x}{10}=-\frac{9}{10} \\ x^2-\frac{x}{10}+(-\frac{1}{20})^2=-\frac{9}{10}+(-\frac{1}{20})^2 \\ (x-\frac{1}{20})^2=-\frac{359}{400}\rightarrow(x-\frac{1}{20})=\sqrt[]{-\frac{359}{400}} \\ x=\frac{1}{20}+i\frac{\sqrt{359}}{20} \\ x=\frac{1}{20}-i\frac{\sqrt{359}}{20} \end{gathered}[/tex]The answer is the last option