Answer
$x_{1}=\dfrac{5 + \sqrt{143}i}{12}$ and $x_{2}=\dfrac{5 - \sqrt{143}i}{12}$
Work Step by Step
Given $6x^2+7=5x \longrightarrow 6x^2-5x+7=0$
$a=6, \ b=-5, \ c=7$
Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a} , $ we have:
$\dfrac{-(-5) \pm \sqrt{(-5)^2-4\times 6\times 7}}{2\times 6} = \dfrac{5 \pm \sqrt{25-168}}{12} = \dfrac{5 \pm \sqrt{-143}}{12} = \dfrac{5 \pm \sqrt{143}i}{12}$
Therefore, the solutions are: $x_{1}=\dfrac{5 + \sqrt{143}i}{12}$ and $x_{2}=\dfrac{5 - \sqrt{143}i}{12}$
