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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

(x+1)

We get rid of parentheses

x+1

Back to the equation:

-(x+1)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+x-1=0

a = 1; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·1·(-1)
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{-(1)-\sqrt{5}}{2*1}=\frac{-1-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*1}=\frac{-1+\sqrt{5}}{2}
$