2(2-4)=x(x+5)

Solution for 2(2-4)=x(x+5) equation:

2(2-4)=x(x+5)

We move all terms to the left:

2(2-4)-(x(x+5))=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-(x(x+5))-4=0


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

x(x+5)

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We get rid of parentheses

-x^2-5x-4=0

We add all the numbers together, and all the variables

-1x^2-5x-4=0

a = -1; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·(-1)·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*-1}=\frac{8}{-2}
=-4
$