585=11x-0.05x^2

Solution for 585=11x-0.05x^2 equation:

585=11x-0.05x^2

We move all terms to the left:

585-(11x-0.05x^2)=0

We get rid of parentheses

0.05x^2-11x+585=0

a = 0.05; b = -11; c = +585;
Δ = b2-4ac
Δ = -112-4·0.05·585
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-2}{2*0.05}=\frac{9}{0.1}
=90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+2}{2*0.05}=\frac{13}{0.1}
=130
$