2x=10x/2x-1

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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 $

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