x=3x/x+3

Solution for x=3x/x+3 equation:

x=3x/x+3

We move all terms to the left:

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


Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

x-3x/x-3=0

We multiply all the terms by the denominator


x*x-3x-3*x=0

We add all the numbers together, and all the variables

-6x+x*x=0

Wy multiply elements

x^2-6x=0

a = 1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*1}=\frac{12}{2}
=6
$