5x/x-4=x

Solution for 5x/x-4=x equation:

5x/x-4=x

We move all terms to the left:

5x/x-4-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5x/x-4=0

We multiply all the terms by the denominator


-1x*x+5x-4*x=0

We add all the numbers together, and all the variables

x-1x*x=0

Wy multiply elements

-1x^2+x=0

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