(X+2)(x+2)+4x=192

Solution for (X+2)(x+2)+4x=192 equation:

(X+2)(X+2)+4X=192

We move all terms to the left:

(X+2)(X+2)+4X-(192)=0

We add all the numbers together, and all the variables

4X+(X+2)(X+2)-192=0

We multiply parentheses ..

(+X^2+2X+2X+4)+4X-192=0

We get rid of parentheses

X^2+2X+2X+4X+4-192=0

We add all the numbers together, and all the variables

X^2+8X-188=0

a = 1; b = 8; c = -188;
Δ = b2-4ac
Δ = 82-4·1·(-188)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{51}}{2*1}=\frac{-8-4\sqrt{51}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{51}}{2*1}=\frac{-8+4\sqrt{51}}{2}
$