find the vertex 6x^(2)+84+294

6 x^2 + 84 x + 294 = y I suspect you mean

x^2 + 14 y = y/6 - 49

x^2 + 14 y + 49 = y/6 -0

(x+7)^2 = (1/6)(y-0)

(-7 , 0 )