#6x^2+9x-6=0#
#"solution 1:"#
#"factor the equation :"#
#3(x+2)(2x-1)=0#
#"if " x+2=0" ; "x=-2#
#"if "2x-1=0" ; "2x=1" ; "x=1/2#
#"solution 2:"#
#"use quadratic formula"#
#ax^2+bx+c=0#
#6x^2+9x-6=0#
#a=6" ; "b=9" ; "c=-6#
#Delta=sqrt(b^2-4*a*c)#
#Delta=sqrt(9^2+4*6*6)#
#Delta=sqrt(81+144)#
#Delta=sqrt(225)#
#x_1=(-9-sqrt(225))/(2*6)=(-9-15)/12=-24/12=-2#
#x_2=(-9+sqrt 225)/(2*6)=(-9+15)/12=6/12=1/2#