8/2x+12=6/x+8

Solution for 8/2x+12=6/x+8 equation:

8/2x+12=6/x+8

We move all terms to the left:

8/2x+12-(6/x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+8)!=0

x∈R


We get rid of parentheses

8/2x-6/x-8+12=0

We calculate fractions


8x/2x^2+(-12x)/2x^2-8+12=0

We add all the numbers together, and all the variables

8x/2x^2+(-12x)/2x^2+4=0

We multiply all the terms by the denominator


8x+(-12x)+4*2x^2=0

Wy multiply elements

8x^2+8x+(-12x)=0

We get rid of parentheses

8x^2+8x-12x=0

We add all the numbers together, and all the variables

8x^2-4x=0

a = 8; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·8·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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