400=5x-(0.01x^2)

Solution for 400=5x-(0.01x^2) equation:

400=5x-(0.01x^2)

We move all terms to the left:

400-(5x-(0.01x^2))=0


We calculate terms in parentheses: -(5x-(0.01x^2)), so:

5x-(0.01x^2)

We get rid of parentheses

-0.01x^2+5x

Back to the equation:

-(-0.01x^2+5x)


We get rid of parentheses

0.01x^2-5x+400=0

a = 0.01; b = -5; c = +400;
Δ = b2-4ac
Δ = -52-4·0.01·400
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{-(-5)-3}{2*0.01}=\frac{2}{0.02}
=100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*0.01}=\frac{8}{0.02}
=400
$