-.5x^2=2x

Solution for -.5x^2=2x equation:

-.5x^2=2x

We move all terms to the left:

-.5x^2-(2x)=0

We add all the numbers together, and all the variables

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