2x/x-3=2x-11/x

Solution for 2x/x-3=2x-11/x equation:

2x/x-3=2x-11/x

We move all terms to the left:

2x/x-3-(2x-11/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x/x-(+2x-11/x)-3=0

We get rid of parentheses

2x/x-2x+11/x-3=0

We multiply all the terms by the denominator


2x-2x*x-3*x+11=0

We add all the numbers together, and all the variables

-1x-2x*x+11=0

Wy multiply elements

-2x^2-1x+11=0

a = -2; b = -1; c = +11;
Δ = b2-4ac
Δ = -12-4·(-2)·11
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{89}}{2*-2}=\frac{1-\sqrt{89}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{89}}{2*-2}=\frac{1+\sqrt{89}}{-4}
$