(x+2)2+12x=3+x(x+2)

Solution for (x+2)2+12x=3+x(x+2) equation:

(x+2)2+12x=3+x(x+2)

We move all terms to the left:

(x+2)2+12x-(3+x(x+2))=0

We add all the numbers together, and all the variables

12x+(x+2)2-(3+x(x+2))=0

We multiply parentheses

12x+2x-(3+x(x+2))+4=0


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

3+x(x+2)

determiningTheFunctionDomain
x(x+2)+3

We multiply parentheses

x^2+2x+3

Back to the equation:

-(x^2+2x+3)


We add all the numbers together, and all the variables

14x-(x^2+2x+3)+4=0

We get rid of parentheses

-x^2+14x-2x-3+4=0

We add all the numbers together, and all the variables

-1x^2+12x+1=0

a = -1; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-1)·1
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{37}}{2*-1}=\frac{-12-2\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{37}}{2*-1}=\frac{-12+2\sqrt{37}}{-2}
$