Solving for a single term.?

You could look into a topic called "completing the square".

Turn the left hand side into a perfect square

y^2 - y + (1/4) = x + 17/4

(y- 1/2)^2 = (4x + 17)/4

square root both sides

(y - 1/2) = sqrt((4x + 17)/4)

or (1/2-y) = sqrt((4x + 17)/4)

Let's take (y - 1/2) = sqrt((4x + 17)/4)

take the -1/2 term to rhs

y = 1/2 + sqrt((4x + 17)/4)

now take (1/2-y) = sqrt((4x + 17)/4)

add y to both sides

1/2 = y + sqrt((4x + 17)/4)

now subtract sqrt((4x + 17)/4) from both sides

1/2 - sqrt((4x + 17)/4) = y

so y = 1/2 - sqrt((4x + 17)/4) or 1/2 + sqrt((4x + 17)/4)

we could simplify it but you see how we solved for y.

y^2 - y = x + 4

(y - 1/2)^2 - 1/4 = x + 4

(y - 1/2)^2 = x + 17/4

y = 1/2 ± √(x + 17/4)

Qardartic eqation

the eqn u wrote is of parabola so i suggest u to read conic section