4/(x+2)+6=14/2x+4

Solution for 4/(x+2)+6=14/2x+4 equation:

4/(x+2)+6=14/2x+4

We move all terms to the left:

4/(x+2)+6-(14/2x+4)=0


Domain of the equation: (x+2)!=0

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

x!=-2

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

4/(x+2)-14/2x-4+6=0

We calculate fractions


8x/(2x^2+4x)+(-14x-28)/(2x^2+4x)-4+6=0

We add all the numbers together, and all the variables

8x/(2x^2+4x)+(-14x-28)/(2x^2+4x)+2=0

We multiply all the terms by the denominator


8x+(-14x-28)+2*(2x^2+4x)=0

We multiply parentheses

4x^2+8x+(-14x-28)+8x=0

We get rid of parentheses

4x^2+8x-14x+8x-28=0

We add all the numbers together, and all the variables

4x^2+2x-28=0

a = 4; b = 2; c = -28;
Δ = b2-4ac
Δ = 22-4·4·(-28)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{113}}{2*4}=\frac{-2-2\sqrt{113}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{113}}{2*4}=\frac{-2+2\sqrt{113}}{8}
$