This equation represents a quadratic function. To solve for y, we can set the equation equal to zero and use the quadratic formula.

b = y^2 - y + 1

Rearranging the equation:

y^2 - y + (1 - b) = 0

Now we can use the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -1, and c = (1 - b) = (1 - (-1)) = 2.

Plugging in these values into the quadratic formula:

y = (-(-1) ± √((-1)^2 - 4(1)(2))) / (2(1))

Simplifying:

y = (1 ± √(1 - 8)) / 2

y = (1 ± √(-7)) / 2

Since the square root of a negative number is not a real number, there are no real solutions for y in this equation.