Answer
$x_{1}=-\dfrac{3}{5} + \dfrac{\sqrt{6}i}{5}$ and $x=-\dfrac{3}{5} - \dfrac{\sqrt{6}i}{5}$
Work Step by Step
Given $5x^2+6x=-3 \longrightarrow 5x^2+6x+3=0$
$a= 5, \ b=6, \ c=3$
Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ we have:
$\dfrac{-6\pm \sqrt{6^2-4\times 5\times 3}}{2 \times 5} = \dfrac{-6\pm \sqrt{36-60}}{10} = \dfrac{-6\pm \sqrt{-24}}{10} = \dfrac{-6\pm \sqrt{4\times (-6)}}{10} = \dfrac{-6\pm 2\sqrt{-6}}{10} =\dfrac{-3\pm \sqrt{-6}}{5} =\dfrac{-3\pm \sqrt{6}i}{5} =\dfrac{-3}{5} \pm \dfrac{\sqrt{6}i}{5}$
Therefore the solutions are $x_{1}=-\dfrac{3}{5} + \dfrac{\sqrt{6}i}{5}$ and $x=-\dfrac{3}{5} - \dfrac{\sqrt{6}i}{5}$
