Answer:
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=-\frac{3}{8}+i\frac{\sqrt{31}}{8},\:x=-\frac{3}{8}-i\frac{\sqrt{31}}{8}[/tex]
Step-by-step explanation:
[tex]8x^2+6x=-5[/tex]
[tex]\mathrm{Add\:}5\mathrm{\:to\:both\:sides}[/tex]
[tex]8x^2+6x+5=-5+5[/tex]
[tex]8x^2+6x+5=0[/tex]
[tex]\underline{\mathrm{Solve\: further\:using\:the\:quadratic\: formula}}[/tex]
[tex]x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:8\cdot \:5}}{2\cdot \:8}[/tex]
[tex]x_{1,\:2}=\frac{-6\pm \:2\sqrt{31}i}{2\cdot \:8}[/tex]
[tex]\mathrm{Separate\:the\:solutions}[/tex]
[tex]x_1=\frac{-6+2\sqrt{31}i}{2\cdot \:8},\:x_2=\frac{-6-2\sqrt{31}i}{2\cdot \:8}[/tex]
[tex]\bold{\frac{-6+2\sqrt{31}i}{2\cdot \:8}=-\frac{3}{8}+\frac{\sqrt{31}}{8}i}[/tex]
[tex]\bold{\frac{-6-2\sqrt{31}i}{2\cdot \:8}=-\frac{3}{8}-\frac{\sqrt{31}}{8}i}[/tex]
More information
Quadratic equation formula:
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
