(3x)/(5-2x)=x

Solution for (3x)/(5-2x)=x equation:

(3x)/(5-2x)=x

We move all terms to the left:

(3x)/(5-2x)-(x)=0


Domain of the equation: (5-2x)!=0

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

-2x!=-5

x!=-5/-2

x!=2+1/2

x∈R


We add all the numbers together, and all the variables

3x/(-2x+5)-x=0

We add all the numbers together, and all the variables

-1x+3x/(-2x+5)=0

We multiply all the terms by the denominator


-1x*(-2x+5)+3x=0

We add all the numbers together, and all the variables

3x-1x*(-2x+5)=0

We multiply parentheses

2x^2+3x-5x=0

We add all the numbers together, and all the variables

2x^2-2x=0

a = 2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·2·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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