The x-interceopt are the values for x where -5x^2+20x+2 = 0. The mistake you made is going from -5x(x-4)+2=0 to -5x(x-4) = 0; what happened to the 2? You should always double check your answers to see if they work. If you plug x=0 or x = 4 into the original equation you get:
so clearly these answers are not right.
Easiest way to find the roots is to apply the quadratic equation: