(X+2)(x+4)=212

Solution for (X+2)(x+4)=212 equation:

(X+2)(X+4)=212

We move all terms to the left:

(X+2)(X+4)-(212)=0

We multiply parentheses ..

(+X^2+4X+2X+8)-212=0

We get rid of parentheses

X^2+4X+2X+8-212=0

We add all the numbers together, and all the variables

X^2+6X-204=0

a = 1; b = 6; c = -204;
Δ = b2-4ac
Δ = 62-4·1·(-204)
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{213}}{2*1}=\frac{-6-2\sqrt{213}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{213}}{2*1}=\frac{-6+2\sqrt{213}}{2}
$