(x+2)(x+1)=x+3

Solution for (x+2)(x+1)=x+3 equation:

(x+2)(x+1)=x+3

We move all terms to the left:

(x+2)(x+1)-(x+3)=0

We get rid of parentheses

(x+2)(x+1)-x-3=0

We multiply parentheses ..

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+2x-1=0

a = 1; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·1·(-1)
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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