x*2+4=(x+1)(x+3)

Solution for x*2+4=(x+1)(x+3) equation:

x*2+4=(x+1)(x+3)

We move all terms to the left:

x*2+4-((x+1)(x+3))=0

Wy multiply elements

2x-((x+1)(x+3))+4=0

We multiply parentheses ..

-((+x^2+3x+x+3))+2x+4=0


We calculate terms in parentheses: -((+x^2+3x+x+3)), so:

(+x^2+3x+x+3)

We get rid of parentheses

x^2+3x+x+3

We add all the numbers together, and all the variables

x^2+4x+3

Back to the equation:

-(x^2+4x+3)


We add all the numbers together, and all the variables

2x-(x^2+4x+3)+4=0

We get rid of parentheses

-x^2+2x-4x-3+4=0

We add all the numbers together, and all the variables

-1x^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}
$