585/2=5*x^2+20*x

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

585/2=5x^2+20x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2-40x+585=0

a = -10; b = -40; c = +585;
Δ = b2-4ac
Δ = -402-4·(-10)·585
Δ = 25000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{25000}=\sqrt{2500*10}=\sqrt{2500}*\sqrt{10}=50\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-50\sqrt{10}}{2*-10}=\frac{40-50\sqrt{10}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+50\sqrt{10}}{2*-10}=\frac{40+50\sqrt{10}}{-20}
$