-4/x=-2/3x-4

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

-4/x=-2/3x-4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2-10x=0

a = 12; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·12·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*12}=\frac{20}{24}
=5/6
$