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

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

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

We move all terms to the left:

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


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

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

x!=-5

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-4x-3=0

a = -1; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·(-1)·(-3)
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{-(-4)-2}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*-1}=\frac{6}{-2}
=-3
$