x*(x+20)=2x*(x+5)

Solution for x*(x+20)=2x*(x+5) equation:

x(x+20)=2x(x+5)

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2x(x+5)), so:

2x(x+5)

We multiply parentheses

2x^2+10x

Back to the equation:

-(2x^2+10x)


We get rid of parentheses

x^2-2x^2+20x-10x=0

We add all the numbers together, and all the variables

-1x^2+10x=0

a = -1; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-1)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-1}=\frac{0}{-2}
=0
$