Answer
$x=\dfrac{5\pm i\sqrt{143}}{12}$
Work Step by Step
Using the properties of equality, the given quadratic equation, $
6x^2+7=5x
,$ is equivalent to
\begin{array}{l}\require{cancel}
6x^2-5x+7=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{-(-5)\pm\sqrt{(-5)^2-4(6)(7)}}{2(6)}
\\\\
x=\dfrac{5\pm\sqrt{25-168}}{12}
\\\\
x=\dfrac{5\pm\sqrt{-143}}{12}
\\\\
x=\dfrac{5\pm\sqrt{-1}\cdot\sqrt{143}}{12}
\\\\
x=\dfrac{5\pm i\sqrt{143}}{12}
.\end{array}
