20/x+6=36/2x-6

Solution for 20/x+6=36/2x-6 equation:

20/x+6=36/2x-6

We move all terms to the left:

20/x+6-(36/2x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

20/x-36/2x+6+6=0

We calculate fractions


40x/2x^2+(-36x)/2x^2+6+6=0

We add all the numbers together, and all the variables

40x/2x^2+(-36x)/2x^2+12=0

We multiply all the terms by the denominator


40x+(-36x)+12*2x^2=0

Wy multiply elements

24x^2+40x+(-36x)=0

We get rid of parentheses

24x^2+40x-36x=0

We add all the numbers together, and all the variables

24x^2+4x=0

a = 24; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·24·0
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*24}=\frac{-8}{48}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*24}=\frac{0}{48}
=0
$