2x=0.5-0.5x^2

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

2x=0.5-0.5x^2

We move all terms to the left:

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

We get rid of parentheses

0.5x^2+2x-0.5=0

a = 0.5; b = 2; c = -0.5;
Δ = b2-4ac
Δ = 22-4·0.5·(-0.5)
Δ = 5
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{-(2)-\sqrt{5}}{2*0.5}=\frac{-2-\sqrt{5}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{5}}{2*0.5}=\frac{-2+\sqrt{5}}{1}
$