(2x)/(x+1)+4x=6

Solution for (2x)/(x+1)+4x=6 equation:

(2x)/(x+1)+4x=6

We move all terms to the left:

(2x)/(x+1)+4x-(6)=0


Domain of the equation: (x+1)!=0

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

x!=-1

x∈R


We add all the numbers together, and all the variables

4x+2x/(x+1)-6=0

We multiply all the terms by the denominator


4x*(x+1)+2x-6*(x+1)=0

We add all the numbers together, and all the variables

2x+4x*(x+1)-6*(x+1)=0

We multiply parentheses

4x^2+2x+4x-6x-6=0

We add all the numbers together, and all the variables

4x^2-6=0

a = 4; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·4·(-6)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*4}=\frac{0-4\sqrt{6}}{8}
=-\frac{4\sqrt{6}}{8}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*4}=\frac{0+4\sqrt{6}}{8}
=\frac{4\sqrt{6}}{8}
=\frac{\sqrt{6}}{2}
$