This is not an equation so there is nothing to solve. But as an expression we can find the zeroes, that is, a solution for x if the expression equals zero.
Completing the square:
2(x²-x/2)-5,
2(x²-x/2+1/16-1/16)-5,
2((x-¼)²-1/16)-5,
2(x-¼)²-⅛-5,
2(x-¼)²-41/8,
2((x-¼)²-41/16),
2(x-¼-√41/4)(x-¼+√41/4).
So x=¼+√41/4 or x=¼-√41/4. This evaluates to x=1.85 or -1.35 approx.