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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+5x+5=0

a = 1; b = 5; c = +5;
Δ = b2-4ac
Δ = 52-4·1·5
Δ = 5
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{-(5)-\sqrt{5}}{2*1}=\frac{-5-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{5}}{2*1}=\frac{-5+\sqrt{5}}{2}
$