Completing the square, you have
.. -2(x^2 -x/2) +5 = 0
.. -2(x^2 -x/2 +1/16) = -5 -1/8 . . . . . add -2*(1/16)
.. (x -1/4)^2 = 2 9/16 . . . . . . . . . . . . divide by -2
.. x = (1 ±√41)/4 . . . . . . . . . . . . . . . .take the square root, add 1/4
.. x ∈ {-1.35078, 1.85072}
