3X squared plus 2X equals -4 number of solutions

Answer:The given equation has two solutions i.e  [tex]\frac{-1+\sqrt{13} }{3}[/tex] ,  [tex]\frac{-1-\sqrt{13} }{3}[/tex] Step-by-step explanation:The given expression as : 3 x² + 2 x - 4For the quadratic equation in the form of a x² + b x + c , the value of x x = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]Or, x =  [tex]\frac{-2\pm \sqrt{2^{2}-4\times 3\times (-4)}}{2\times 3}[/tex]Or, x = [tex]\frac{-2\pm \sqrt{4 + 48}}{6}[/tex]or, x = [tex]\frac{-2\pm \sqrt{52}}{6}[/tex]∴ x = [tex]\frac{-1\pm \sqrt{13}}{3}[/tex]Or, x = [tex]\frac{-1+\sqrt{13} }{3}[/tex] ,  [tex]\frac{-1-\sqrt{13} }{3}[/tex]Hence The given equation has two solutions i.e  [tex]\frac{-1+\sqrt{13} }{3}[/tex] ,  [tex]\frac{-1-\sqrt{13} }{3}[/tex]  Answer