9x/6x+3=x

Solution for 9x/6x+3=x equation:

9x/6x+3=x

We move all terms to the left:

9x/6x+3-(x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+9x/6x+3=0

We multiply all the terms by the denominator


-1x*6x+9x+3*6x=0

We add all the numbers together, and all the variables

9x-1x*6x+3*6x=0

Wy multiply elements

-6x^2+9x+18x=0

We add all the numbers together, and all the variables

-6x^2+27x=0

a = -6; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-6)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-6}=\frac{-54}{-12}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-6}=\frac{0}{-12}
=0
$