Answer
{$\dfrac{3}{8}-\dfrac{\sqrt{87}}{8}i,\dfrac{3}{8} + \dfrac{\sqrt{87}}{8}i$}
Work Step by Step
Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
Since, $4x^2-3x+6=0$
Thus, $x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(4)(6)}}{2(4)}$
or, $x=\dfrac{3 \pm \sqrt{-87}}{8}$
or, $x=\dfrac{3}{8} \pm \dfrac{\sqrt{87}}{8}i$
or, $x=\dfrac{3}{8}-\dfrac{\sqrt{87}}{8}i,\dfrac{3}{8} + \dfrac{\sqrt{87}}{8}i$
Our solution set is: {$\dfrac{3}{8}-\dfrac{\sqrt{87}}{8}i,\dfrac{3}{8} + \dfrac{\sqrt{87}}{8}i$}
