Explanation:
4x + y^2 + 2y = - 5
4x = - y^2 -2y - 5
4x = - (y^2 + 2y) - 5 'complete the square' for y
4x = - ( y +1)^2 + 1 - 5
x = - 1/4 ( y+1)^2 - 1 vertex is at -1, -1
-14x+2y^2-8y -20 = 0
14x = 2y^2 -8y-20
14x = 2 ( y^2 - 4y) - 20 complete the square for y
14x = 2(y-2)^2 -8 - 20
x = 1/7 ( y-2)^2 - 2 Vertex is at -2 , 2