5x^2 + 4x - 2 = 0

How would you solve this by graphing?

Do you just draw a graph by finding x and y?
The answer is -(2-sqrt14)/5, -(2+sqrt14)/5

There's no way you can just graph it and come up with these numbers by finding the integers of x. How would you do this?

a graphing solution is only ever approximate, depending on how accurately you can draw the graph. There are lots of online graphing sites, such as desmos and wolframalpha.