How do you solve the quadratic #6x^2+9x-6=0# using any method?

1 Answer
Oct 12, 2016

Answer:

#x={-2,1/2}#

Explanation:

#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#