2/x+3=12/2x-8

Solution for 2/x+3=12/2x-8 equation:

2/x+3=12/2x-8

We move all terms to the left:

2/x+3-(12/2x-8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-8)!=0

x∈R


We get rid of parentheses

2/x-12/2x+8+3=0

We calculate fractions


4x/2x^2+(-12x)/2x^2+8+3=0

We add all the numbers together, and all the variables

4x/2x^2+(-12x)/2x^2+11=0

We multiply all the terms by the denominator


4x+(-12x)+11*2x^2=0

Wy multiply elements

22x^2+4x+(-12x)=0

We get rid of parentheses

22x^2+4x-12x=0

We add all the numbers together, and all the variables

22x^2-8x=0

a = 22; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·22·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*22}=\frac{0}{44}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*22}=\frac{16}{44}
=4/11
$