500=6x-(.01x^2)

Solution for 500=6x-(.01x^2) equation:

500=6x-(.01x^2)

We move all terms to the left:

500-(6x-(.01x^2))=0


We calculate terms in parentheses: -(6x-(.01x^2)), so:

6x-(.01x^2)

We get rid of parentheses

-.01x^2+6x

We add all the numbers together, and all the variables

-0.01x^2+6x

Back to the equation:

-(-0.01x^2+6x)


We get rid of parentheses

0.01x^2-6x+500=0

a = 0.01; b = -6; c = +500;
Δ = b2-4ac
Δ = -62-4·0.01·500
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*0.01}=\frac{2}{0.02}
=100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*0.01}=\frac{10}{0.02}
=500
$