Answer
Solutions:
$x=-\frac{1}{4}+\frac{\sqrt {71}}{4}i$
$x=-\frac{1}{4}-\frac{\sqrt {71}}{4}i$
Work Step by Step
$6x^2+3x+27=0~~$ ($a=6,b=3,c=27$):
$x=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-3±\sqrt {3^2-4(6)(27)}}{2(6)}=\frac{-3±\sqrt {-639}}{12}=\frac{-3±3\sqrt {71}i}{12}=-\frac{1}{4}±\frac{\sqrt {71}}{4}i$
$x=-\frac{1}{4}+\frac{\sqrt {71}}{4}i$ or $x=-\frac{1}{4}-\frac{\sqrt {71}}{4}i$
