0=x^2-x-0.5

Solution for 0=x^2-x-0.5 equation:

0=x^2-x-0.5

We move all terms to the left:

0-(x^2-x-0.5)=0

We add all the numbers together, and all the variables

-(x^2-x-0.5)=0

We get rid of parentheses

-x^2+x+0.5=0

We add all the numbers together, and all the variables

-1x^2+x+0.5=0

a = -1; b = 1; c = +0.5;
Δ = b2-4ac
Δ = 12-4·(-1)·0.5
Δ = 3
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{3}}{2*-1}=\frac{-1-\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{3}}{2*-1}=\frac{-1+\sqrt{3}}{-2}
$