2x/x-5=x

Solution for 2x/x-5=x equation:

2x/x-5=x

We move all terms to the left:

2x/x-5-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2x/x-5=0

We multiply all the terms by the denominator


-1x*x+2x-5*x=0

We add all the numbers together, and all the variables

-3x-1x*x=0

Wy multiply elements

-1x^2-3x=0

a = -1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-1}=\frac{6}{-2}
=-3
$