`3x^2=3-4x`

Rearrange:

`3x^2+4x=3`

Divide throughout by 3:

`x^2+4/3x=1`

Write left hand side as a perfect square:

`x^2+4/3x+(2/3)^2=1+(2/3)^2`

`(x+2/3)^2=1+4/9=13/9`

Solve:

`x+2/3=+-sqrt(13/9)=+-sqrt(13)/3`

`x=-2/3+-sqrt(13)/3`

`x=-1.869\ "or"\ x=0.535`

Easy to understand math videos:
MathTutorDVD.com