x/(x+4)+4(x+4)+2=0

Solution for x/(x+4)+4(x+4)+2=0 equation:

x/(x+4)+4(x+4)+2=0


Domain of the equation: (x+4)!=0

We move all terms containing x to the left, all other terms to the right

x!=-4

x∈R


We multiply parentheses

x/(x+4)+4x+16+2=0

We multiply all the terms by the denominator


x+4x*(x+4)+16*(x+4)+2*(x+4)=0

We multiply parentheses

4x^2+x+16x+16x+2x+64+8=0

We add all the numbers together, and all the variables

4x^2+35x+72=0

a = 4; b = 35; c = +72;
Δ = b2-4ac
Δ = 352-4·4·72
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{73}}{2*4}=\frac{-35-\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{73}}{2*4}=\frac{-35+\sqrt{73}}{8}
$