Answer
The solutions are $6+3i\sqrt{6}$ and $6-3i\sqrt{6}$.
Work Step by Step
$ 0.1x^{2}-x+9=0.2x\qquad$ ...add $-0.2x$ to each side
$ 0.1x^{2}-1.2x+9=0\qquad$ ...write the expression in the form $ax^{2}+bx=c$
$ 0.1x^{2}-1.2x=-9\qquad$ ...multiply the entire expression with $10$.
$ x^{2}-12x=90\qquad$ ...square half the coefficient of $x$.
$(\displaystyle \frac{-12}{2})^{2}=(6)^{2}=36\qquad$ ...complete the square by adding $36$ to each side of the expression
$ x^{2}-12x+36=-90+36\qquad$ ...Write $x^{2}-12x+36$ as a binomial squared.
$(x-6)^{2}=-54\qquad$ ...take square roots of each side.
$ x-6=\pm\sqrt{-54}\qquad$ ...simplify $\sqrt{-54}=i\sqrt{54}=i\sqrt{9\cdot 6}=3i\sqrt{6}$
$ x-6=\pm 3i\sqrt{6}\qquad$ ...add $6$ to each side.
$x=6\pm 3i\sqrt{6}$
