0.5x^2=-2x

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

0.5x^2=-2x

We move all terms to the left:

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

We get rid of parentheses

0.5x^2+2x=0

a = 0.5; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·0.5·0
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{-(2)-2}{2*0.5}=\frac{-4}{1}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*0.5}=\frac{0}{1}
=0
$