x=100x-0.5x^2

Solution for x=100x-0.5x^2 equation:

x=100x-0.5x^2

We move all terms to the left:

x-(100x-0.5x^2)=0

We get rid of parentheses

0.5x^2-100x+x=0

We add all the numbers together, and all the variables

0.5x^2-99x=0

a = 0.5; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·0.5·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*0.5}=\frac{0}{1}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*0.5}=\frac{198}{1}
=198
$