585=5*x^2+20*x

Solution for 585=5*x^2+20*x equation:

585=5x^2+20x

We move all terms to the left:

585-(5x^2+20x)=0

We get rid of parentheses

-5x^2-20x+585=0

a = -5; b = -20; c = +585;
Δ = b2-4ac
Δ = -202-4·(-5)·585
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-110}{2*-5}=\frac{-90}{-10}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+110}{2*-5}=\frac{130}{-10}
=-13
$