0=0.5x^2+1x

Solution for 0=0.5x^2+1x equation:

0=0.5x^2+1x

We move all terms to the left:

0-(0.5x^2+1x)=0

We add all the numbers together, and all the variables

-(0.5x^2+1x)=0

We get rid of parentheses

-0.5x^2-1x=0

a = -0.5; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-0.5)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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