(x+4)(2x+4)=118

Solution for (x+4)(2x+4)=118 equation:

(x+4)(2x+4)=118

We move all terms to the left:

(x+4)(2x+4)-(118)=0

We multiply parentheses ..

(+2x^2+4x+8x+16)-118=0

We get rid of parentheses

2x^2+4x+8x+16-118=0

We add all the numbers together, and all the variables

2x^2+12x-102=0

a = 2; b = 12; c = -102;
Δ = b2-4ac
Δ = 122-4·2·(-102)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{15}}{2*2}=\frac{-12-8\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{15}}{2*2}=\frac{-12+8\sqrt{15}}{4}
$