(x+2)2-x2=4(x+1)

Solution for (x+2)2-x2=4(x+1) equation:

(x+2)2-x2=4(x+1)

We move all terms to the left:

(x+2)2-x2-(4(x+1))=0

We add all the numbers together, and all the variables

-1x^2+(x+2)2-(4(x+1))=0

We multiply parentheses

-1x^2+2x-(4(x+1))+4=0


We calculate terms in parentheses: -(4(x+1)), so:

4(x+1)

We multiply parentheses

4x+4

Back to the equation:

-(4x+4)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-2x=0

a = -1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-1}=\frac{4}{-2}
=-2
$