6x/3x+5=x

Solution for 6x/3x+5=x equation:

6x/3x+5=x

We move all terms to the left:

6x/3x+5-(x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+6x/3x+5=0

We multiply all the terms by the denominator


-1x*3x+6x+5*3x=0

We add all the numbers together, and all the variables

6x-1x*3x+5*3x=0

Wy multiply elements

-3x^2+6x+15x=0

We add all the numbers together, and all the variables

-3x^2+21x=0

a = -3; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-3)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-3}=\frac{0}{-6}
=0
$