x=-0.5x2+x+2

Solution for x=-0.5x2+x+2 equation:

x=-0.5x^2+x+2

We move all terms to the left:

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

We get rid of parentheses

0.5x^2-x+x-2=0

We add all the numbers together, and all the variables

0.5x^2-2=0

a = 0.5; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·0.5·(-2)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2}{2*0.5}=\frac{-2}{1}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2}{2*0.5}=\frac{2}{1}
=2
$