The x-coordinate of the vertex will be = -b/(2a) when you're given an equation of the form y = ax^2 + bx + c.
So here a = 3, b = 18, and so the x-coord is -18/(2*3) = -3.
Now just plug that into the equation to find the y-coord of the vertex:
3(-3)^2 + 18(-3) + 10 = -17
So the vertex is (-3,-17)