(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

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-6x=0

a = 8; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·8·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*8}=\frac{12}{16}
=3/4
$