The original problem:
Quadratic formula gives
That's what I get. WolframAlpha gives the same.
I conclude your book's answer is wrong.
-3/4(+-)SQRT((3/4^2)-4(1/2)(-1) / 2(1/2)
-3/4(+-)SQRT(9/16+2) / 1
This is as far as I can get I do not see any errors yet the answer is supposed to be
I am clueless as to where the 41 comes from
GOOD IDEA to always get rid of fractions before doing anything else;
so multiply your equation by 4: 2x^2 + 3x - 4 = 0 : get the picture?
Now use the quadratic and you'll have no problems