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

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

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

We move all terms to the left:

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


Domain of the equation: x+6)!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2+8x+(-14x)=0

We get rid of parentheses

16x^2+8x-14x=0

We add all the numbers together, and all the variables

16x^2-6x=0

a = 16; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·16·0
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*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*16}=\frac{12}{32}
=3/8
$