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

Solution for (x-1)/(2-x)=2x=1 equation:

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

We move all terms to the left:

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


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

We move all terms containing x to the left, all other terms to the right

-x!=-2

x!=-2/-1

x!=+2

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-2x*(-1x+2)+(x-1)=0

We multiply parentheses

2x^2-4x+(x-1)=0

We get rid of parentheses

2x^2-4x+x-1=0

We add all the numbers together, and all the variables

2x^2-3x-1=0

a = 2; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·2·(-1)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{17}}{2*2}=\frac{3-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*2}=\frac{3+\sqrt{17}}{4}
$