Answer
$x=\dfrac{1\pm i\sqrt{35}}{9}$
Work Step by Step
Using the properties of equality, the given quadratic equation, $
9x^2+4=2x
,$ is equivalent to
\begin{array}{l}\require{cancel}
9x^2-2x+4=0
.\end{array}
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the quadratic equation above are
\begin{array}{l}\require{cancel}
x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(9)(4)}}{2(9)}
\\\\
x=\dfrac{2\pm\sqrt{4-144}}{18}
\\\\
x=\dfrac{2\pm\sqrt{-140}}{18}
\\\\
x=\dfrac{2\pm\sqrt{-1}\cdot\sqrt{140}}{18}
\\\\
x=\dfrac{2\pm i\sqrt{4\cdot35}}{18}
\\\\
x=\dfrac{2\pm i\sqrt{(2)62\cdot35}}{18}
\\\\
x=\dfrac{2\pm 2i\sqrt{35}}{18}
\\\\
x=\dfrac{2(1\pm i\sqrt{35})}{18}
\\\\
x=\dfrac{\cancel{2}(1\pm i\sqrt{35})}{\cancel{2}(9)}
\\\\
x=\dfrac{1\pm i\sqrt{35}}{9}
.\end{array}
