x+(x+5)=(x+1)(x+2)

Solution for x+(x+5)=(x+1)(x+2) equation:

x+(x+5)=(x+1)(x+2)

We move all terms to the left:

x+(x+5)-((x+1)(x+2))=0

We get rid of parentheses

x+x-((x+1)(x+2))+5=0

We multiply parentheses ..

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


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

(+x^2+2x+x+2)

We get rid of parentheses

x^2+2x+x+2

We add all the numbers together, and all the variables

x^2+3x+2

Back to the equation:

-(x^2+3x+2)


We add all the numbers together, and all the variables

2x-(x^2+3x+2)+5=0

We get rid of parentheses

-x^2+2x-3x-2+5=0

We add all the numbers together, and all the variables

-1x^2-1x+3=0

a = -1; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-1)·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{13}}{2*-1}=\frac{1-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*-1}=\frac{1+\sqrt{13}}{-2}
$