[tex]2x^2 + 3x = -5\\2x^2 + 3x +5=0\\ \Delta=3^2-4\cdot2\cdot5=9-40=-31\\\\\Delta<0\ \Rightarrow\ no\ real\ solution\\\\ \Delta=-31\ \ \ \Rightarrow\ \ \ \Delta=31\cdot(-1)= \sqrt{31} ^2\cdot i^2=( \sqrt{31} \ i)^2\\\\x= \frac{\big{-3\pm \sqrt{\Delta} }}{\big{2\cdot2}} =\frac{\big{-3\pm \sqrt{31}\ i }}{\big{4}}[/tex]
