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+11=0

We multiply all the terms by the denominator


2x+(-3x)+11*3x^2=0

Wy multiply elements

33x^2+2x+(-3x)=0

We get rid of parentheses

33x^2+2x-3x=0

We add all the numbers together, and all the variables

33x^2-1x=0

a = 33; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·33·0
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*33}=\frac{0}{66}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*33}=\frac{2}{66}
=1/33
$