x=0.5x^2+4x

Solution for x=0.5x^2+4x equation:

x=0.5x^2+4x

We move all terms to the left:

x-(0.5x^2+4x)=0

We get rid of parentheses

-0.5x^2+x-4x=0

We add all the numbers together, and all the variables

-0.5x^2-3x=0

a = -0.5; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-0.5)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-0.5}=\frac{0}{-1}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-0.5}=\frac{6}{-1}
=-6
$