2/3x=8/2x+10

Solution for 2/3x=8/2x+10 equation:

2/3x=8/2x+10

We move all terms to the left:

2/3x-(8/2x+10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+10)!=0

x∈R


We get rid of parentheses

2/3x-8/2x-10=0

We calculate fractions


4x/6x^2+(-24x)/6x^2-10=0

We multiply all the terms by the denominator


4x+(-24x)-10*6x^2=0

Wy multiply elements

-60x^2+4x+(-24x)=0

We get rid of parentheses

-60x^2+4x-24x=0

We add all the numbers together, and all the variables

-60x^2-20x=0

a = -60; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-60)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-60}=\frac{40}{-120}
=-1/3
$