Answer
$x=\dfrac{3}{8}\pm\dfrac{\sqrt{87}}{8}i$
Work Step by Step
$6=-4x^{2}+3x$
Rewrite the equation by taking all terms to the left side of the equation:
$4x^{2}-3x+6=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=4$, $b=-3$ and $c=6$
Substitute:
$x=\dfrac{-(-3)\pm\sqrt{(-3)^{2}-4(4)(6)}}{2(4)}=\dfrac{3\pm\sqrt{9-96}}{8}=...$
$...=\dfrac{3\pm\sqrt{-87}}{8}=\dfrac{3\pm\sqrt{87}i}{8}=\dfrac{3}{8}\pm\dfrac{\sqrt{87}}{8}i$
