2/3x-10=4/2x+4

Solution for 2/3x-10=4/2x+4 equation:

2/3x-10=4/2x+4

We move all terms to the left:

2/3x-10-(4/2x+4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

2/3x-4/2x-4-10=0

We calculate fractions


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

We add all the numbers together, and all the variables

4x/6x^2+(-12x)/6x^2-14=0

We multiply all the terms by the denominator


4x+(-12x)-14*6x^2=0

Wy multiply elements

-84x^2+4x+(-12x)=0

We get rid of parentheses

-84x^2+4x-12x=0

We add all the numbers together, and all the variables

-84x^2-8x=0

a = -84; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-84)·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*-84}=\frac{0}{-168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-84}=\frac{16}{-168}
=-2/21
$