If \(2x^2+6x+17=0\) then the quadratic formula gives the two solutions:
\(x=\dfrac{-6\pm\sqrt{36-4(2)(17)}}{4}=\dfrac{-6\pm\sqrt{-100}}{4}=\dfrac{-6\pm10i}{4}=-\dfrac{3}{2}\pm\dfrac{5}{2}i\)