Finding Area Between x=2(y^2) & x+y=1

[fk378]

Homework Statement

Find the area between
x=2(y^2) and x+y=1

The Attempt at a Solution

First I'm trying to find their intersection so

To solve for y I set up:
2(y^2)=1-y
2(y^2)+y=1
y=0,1

But, I notice that my teacher did:
2(y^2)+y-1=0
(2y+1)(y-1)=0
y=-1, 1/2

Why are these 2 methods bringing about different answers? Shouldn't they be the same?

 

[Dick]

Don't double post.