4/6x-20=2/x+10

Solution for 4/6x-20=2/x+10 equation:

4/6x-20=2/x+10

We move all terms to the left:

4/6x-20-(2/x+10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: x+10)!=0

x∈R


We get rid of parentheses

4/6x-2/x-10-20=0

We calculate fractions


4x/6x^2+(-12x)/6x^2-10-20=0

We add all the numbers together, and all the variables

4x/6x^2+(-12x)/6x^2-30=0

We multiply all the terms by the denominator


4x+(-12x)-30*6x^2=0

Wy multiply elements

-180x^2+4x+(-12x)=0

We get rid of parentheses

-180x^2+4x-12x=0

We add all the numbers together, and all the variables

-180x^2-8x=0

a = -180; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-180)·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*-180}=\frac{0}{-360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-180}=\frac{16}{-360}
=-2/45
$