(x+4)(x+4+3x)=216

Solution for (x+4)(x+4+3x)=216 equation:

(x+4)(x+4+3x)=216

We move all terms to the left:

(x+4)(x+4+3x)-(216)=0

We add all the numbers together, and all the variables

(x+4)(4x+4)-216=0

We multiply parentheses ..

(+4x^2+4x+16x+16)-216=0

We get rid of parentheses

4x^2+4x+16x+16-216=0

We add all the numbers together, and all the variables

4x^2+20x-200=0

a = 4; b = 20; c = -200;
Δ = b2-4ac
Δ = 202-4·4·(-200)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-60}{2*4}=\frac{-80}{8}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+60}{2*4}=\frac{40}{8}
=5
$