2(y)^2 - 3y = x + 2
2(Y)^2 - 3Y - K = 0 (K = X+2)
Y^2 - (3/2)Y - K/2 = 0
(Y - 3/4)(Y - 3/4) - K/2 - 9/16 = 0
(Y - 3/4)^2 - (K/2 + 9/16) = 0
(Y - 3/4)^2 = (K/2 + 9/16)
Y - 3/4 = sqrt(K/2 + 9/16)
Y = 3/4 + sqrt(K/2 + 9/16)
Y = 3/4 + sqrt((X + 2)/2 + 9/16)
Y = 3/4 + sqrt((8X + 16)/16 + 9/16)
Y = 3/4 + sqrt((8X + 16 + 9)/16)
Y = sqrt((8X + 25)/16)
Y = (3 +/- sqrt(8X + 25))/4
WHY do all that work? Never heard of the quadratic formula?
2y^2 - 3y - k = 0 , where k = x + 2
y = {-(-3) +/- SQRT[(-3)^2 - 4(2)(-k)]} / 4
y = [3 +/- SQRT(9 + 8k)] / 4
Substitute k = x + 2:
y = [3 +/- SQRT(9 + 8(x + 2))] / 4
y = [3 +/- SQRT(8x + 25)] / 4
Done!