30000x=-0.5x^2+400x-400x

Solution for 30000x=-0.5x^2+400x-400x equation:

30000x=-0.5x^2+400x-400x

We move all terms to the left:

30000x-(-0.5x^2+400x-400x)=0

We get rid of parentheses

0.5x^2-400x+400x+30000x=0

We add all the numbers together, and all the variables

0.5x^2+30000x=0

a = 0.5; b = 30000; c = 0;
Δ = b2-4ac
Δ = 300002-4·0.5·0
Δ = 900000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900000000}=30000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30000)-30000}{2*0.5}=\frac{-60000}{1}
=-60000
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30000)+30000}{2*0.5}=\frac{0}{1}
=0
$