10/x-1=2x

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

10/x-1=2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+10/x-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -2; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-2)·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-2}=\frac{10}{-4}
=-2+1/2
$