Algebra 2 Common Core

$$\text{A}$$
Recall: A quadratic equation in the form $ax^2+bx+c=0$ can be solved using the Quadratic Formula: $$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$$ The given quadratic equation has $a=6, b=-10,$ and $c=3$. Use these values and the quadratic formula to obtain: \begin{align*} x&=\dfrac{-(-10)\pm\sqrt{(-10)^2-4(6)(3)}}{2(6)}\\\\ &=\dfrac{10\pm \sqrt{100-72}}{12}\\\\ &=\dfrac{10\pm \sqrt{28}}{12}\\\\ &=\dfrac{10\sqrt{4(7)}}{12}\\\\ &=\dfrac{10\pm 2\sqrt7}{12} \end{align*} Cancel out the common factor of $2$ to obtain: \begin{align*} \require{cancel} x&=\dfrac{\cancel{10}^5\pm \cancel{2}\sqrt7}{\cancel{12}^6}\\ &=\dfrac{5\pm \sqrt7}{6} \end{align*} Thus, the answer is Option $\text{A}$.