Question

`3x^2-x-2=0` 

Answer 1

`3x^2-x-2=0` 

`9x^2-3x-6=0`                       (Multiplying both sides by 3) 

`9x^2-3x=6`  

`(3x)^2-2xx3x xx1/2+(1/2)^2=6(1/2)^2`          [Adding `(1/2)^2` on both sides] 

`(3x-1/2)^2=6+1/4=25/4=(5/2)^2` 

`3x-1/2=+-5/2`                (Taking square root on both sides)

`3x-1/2=5/2  or  3x-1/2=-5/2` 

`3x=5/2+1/2=6/2=3  or  =-5/2+1/2=-4/2=-2` 

`x=1  or  x=-2/3` 

Hence, 1 and `-2/3` are the roots of the given equation.