[tex] 2x^2 + x - 15 =0\\ \\a=2 , \ b = 1 , \ c= -15 \\ \\\Delta = b^{2}-4ac = 1^{2}-4*2* (-15)=1 +120 = 121 \\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{-1-\sqrt{121}}{ 2*2}=\frac{-1-11}{4}=\frac{-12 }{4 }= -3\\ \\ x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{-1+\sqrt{121}}{ 2*2}=\frac{-1+11}{4}=\frac{10}{4 }= \frac{5}{2} \\ \\ \\ Answer : \ 2x^2 + x-15 = (x+3)(x-\frac{5}{2})[/tex]
