Answer
The solutions are $x=-\dfrac{1}{4}\pm\dfrac{\sqrt{39}}{12}i$
Work Step by Step
$-6x^{2}=3x+2$
Take all terms to the left side of the equation:
$-6x^{2}-3x-2=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In this case, $a=-6$, $b=-3$ and $c=-2$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-3)\pm\sqrt{(-3)^{2}-4(-6)(-2)}}{2(-6)}=\dfrac{3\pm\sqrt{9-48}}{-12}=...$
$...=\dfrac{3\pm\sqrt{-39}}{-12}=\dfrac{3\pm\sqrt{39}i}{-12}=-\dfrac{3}{12}\pm\dfrac{\sqrt{39}}{12}i=...$
$...=-\dfrac{1}{4}\pm\dfrac{\sqrt{39}}{12}i$
The solutions are $x=-\dfrac{1}{4}\pm\dfrac{\sqrt{39}}{12}i$
