4-2x/3x=-1-2x/2=10+x/9

Solution for 4-2x/3x=-1-2x/2=10+x/9 equation:

4-2x/3x=-1-2x/2=10+x/9

We move all terms to the left:

4-2x/3x-(-1-2x/2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x/3x-(-2x/2-1)+4=0

We get rid of parentheses

-2x/3x+2x/2+1+4=0

We calculate fractions


6x^2/6x+(-4x)/6x+1+4=0

We add all the numbers together, and all the variables

6x^2/6x+(-4x)/6x+5=0

We multiply all the terms by the denominator


6x^2+(-4x)+5*6x=0

Wy multiply elements

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

We get rid of parentheses

6x^2-4x+30x=0

We add all the numbers together, and all the variables

6x^2+26x=0

a = 6; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·6·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*6}=\frac{-52}{12}
=-4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*6}=\frac{0}{12}
=0
$