[tex] 2x^{2} -3x-2=0\\\Delta=b^2-4*a*c=(-3)^2-4*2*(-2)=9+16=25\\
x_1= \frac{-b-\sqrt{\Delta}}{2*a}= \frac{3-5}{4}= \frac{-2}{4}= -\frac{1}{2}\\
x_2= \frac{-b+\sqrt{\Delta}}{2*a}= \frac{3+5}{4}= \frac{8}{4}= 2\\
a x^{2} +bx+c=a(x-x_1)(x-x_2)\\
2 x^{2} -3x-2=2(x+ \frac{1}{2})(x-2)[/tex]
