500=(x+5)(x)

Solution for 500=(x+5)(x) equation:

500=(x+5)(x)

We move all terms to the left:

500-((x+5)(x))=0


We calculate terms in parentheses: -((x+5)x), so:

(x+5)x

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We get rid of parentheses

-x^2-5x+500=0

We add all the numbers together, and all the variables

-1x^2-5x+500=0

a = -1; b = -5; c = +500;
Δ = b2-4ac
Δ = -52-4·(-1)·500
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-45}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+45}{2*-1}=\frac{50}{-2}
=-25
$