(x)(x+2)+(x)+(x+2)=119

Solution for (x)(x+2)+(x)+(x+2)=119 equation:

(x)(x+2)+(x)+(x+2)=119

We move all terms to the left:

(x)(x+2)+(x)+(x+2)-(119)=0

We add all the numbers together, and all the variables

x+x(x+2)+(x+2)-119=0

We multiply parentheses

x^2+x+2x+(x+2)-119=0

We get rid of parentheses

x^2+x+2x+x+2-119=0

We add all the numbers together, and all the variables

x^2+4x-117=0

a = 1; b = 4; c = -117;
Δ = b2-4ac
Δ = 42-4·1·(-117)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-22}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+22}{2*1}=\frac{18}{2}
=9
$