The x- intercepts are the points at which y is equal to zero, so you set the right hand side of your equation equal to zero. You can then multiply both sides by the denominator x^2-4x+3 which leaves you with just 0=2x^2+5x+2. When you factor you get 0=(x+2)(2x+1) which gives you x= -0.5 or -2.
