2x=10x/2x-1

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

2x=10x/2x-1

We move all terms to the left:

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


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2x*2x-10x+1*2x=0

We add all the numbers together, and all the variables

-10x+2x*2x+1*2x=0

Wy multiply elements

4x^2-10x+2x=0

We add all the numbers together, and all the variables

4x^2-8x=0

a = 4; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·4·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*4}=\frac{16}{8}
=2
$