It's always a good idea to check your answer by substituting your solution for x back into the original equation to see if it works. This will give you confidence that you have the right answer or let you know if you need to try again. All professionals will do this.

In most practical problems you will rarely get an answer that has a nice whole number as the result. So if you don't get one it still may be correct. Just check it.

Good job on making a solid attempt to solve this problem!

See Nataliya's answer for the full explanation. The key point where you went wrong was on b². The b value is -1, which means the entire value including the negative sign is being squared, (-1)²=1. So the value under the radical should have been 1+80=81 and you accidentally ended up with -1+80=79.

ax² + bx + c = 0 ; x_1,2 = (-b ± √D)/2a ; D = b² - 4ac .
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2x² - x - 10 = 0
D = (-1)² - 4 · 2 · (-10) = 1 + 80 = 81
x₁ = (-(-1) + √81)/4 = (1 + 9)/4 = 5/2 = 2.5
x₂ = (-(-1) - √81)/4 = (1 - 9)/4 = -2