x=-1/3x+9

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

x=-1/3x+9

We move all terms to the left:

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


Domain of the equation: 3x+9)!=0

x∈R


We get rid of parentheses

x+1/3x-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 = 717
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{717}}{2*3}=\frac{27-\sqrt{717}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{717}}{2*3}=\frac{27+\sqrt{717}}{6}
$