0=-0.5x^2+100x

Solution for 0=-0.5x^2+100x equation:

0=-0.5x^2+100x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

0.5x^2-100x=0

a = 0.5; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·0.5·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*0.5}=\frac{0}{1}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*0.5}=\frac{200}{1}
=200
$