1/3x=9+1x

Solution for 1/3x=9+1x equation:

1/3x=9+1x

We move all terms to the left:

1/3x-(9+1x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(x+9)=0

We get rid of parentheses

1/3x-x-9=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2-27x+1=0

a = -3; b = -27; c = +1;
Δ = b2-4ac
Δ = -272-4·(-3)·1
Δ = 741
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{741}}{2*-3}=\frac{27-\sqrt{741}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{741}}{2*-3}=\frac{27+\sqrt{741}}{-6}
$