x^2-x=0.5

Solution for x^2-x=0.5 equation:

x^2-x=0.5

We move all terms to the left:

x^2-x-(0.5)=0

We add all the numbers together, and all the variables

x^2-1x-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}
$