f(x) = x^2 - 4x + 3 and g(x)= 2x - 1
x^2 - 4x + 3 = 2x - 1
x^2 - 6x = -4
x^2 - x = -2/3
and now I'm stuck?
How do i get rid of x^2 - x?
Your steps are wrong.
Try to remove all terms from one side and put them onto the other side, using the inverses of the terms. Simplify the resulting expression.
..., in fact, I see you mistake. You improperly divided almost both sides by 3. That is no help. Go back to the line, x^2-6x=-4 and continue from this. You would want to get all terms on one side of the equation and you will have a quadratic equation. From there, use general solution to a quadratic formula.
You should not ask, "how do I get rid of x^2-x". You should not want to get rid of it. That is part of the quadratic expression in the resulting quadratic equation which you would solve through the general solution.