20=x*(x+1)

Solution for 20=x*(x+1) equation:

20=x(x+1)

We move all terms to the left:

20-(x(x+1))=0


We calculate terms in parentheses: -(x(x+1)), so:

x(x+1)

We multiply parentheses

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2-x+20=0

We add all the numbers together, and all the variables

-1x^2-1x+20=0

a = -1; b = -1; c = +20;
Δ = b2-4ac
Δ = -12-4·(-1)·20
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-1}=\frac{10}{-2}
=-5
$