i need help with this one i've tried it many ways and still can't figure it out because it has the lines going between two solid lines.

find the x-intercepts.
y = x^2 +5x+2

x intercepts is when y is zero.

0=x^2 +5x+2

using formula

5/2 +- 1/2 sqrt (25-8)

that is the answer. I don't know what you mean by lines going between..
This graph is parabola, not a line. However, you don't need to graph it at all, just use the solution above.

so then my answer would be

(5+-sqrt(17))/2,0)and (0,5+-sqrt(17))/(2)