2/3x-10=1/x-1

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

2/3x-10=1/x-1

We move all terms to the left:

2/3x-10-(1/x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

2/3x-1/x+1-10=0

We calculate fractions


2x/3x^2+(-3x)/3x^2+1-10=0

We add all the numbers together, and all the variables

2x/3x^2+(-3x)/3x^2-9=0

We multiply all the terms by the denominator


2x+(-3x)-9*3x^2=0

Wy multiply elements

-27x^2+2x+(-3x)=0

We get rid of parentheses

-27x^2+2x-3x=0

We add all the numbers together, and all the variables

-27x^2-1x=0

a = -27; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-27)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-27}=\frac{0}{-54}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-27}=\frac{2}{-54}
=-1/27
$