(1/3)(9-x)-6=x

Solution for (1/3)(9-x)-6=x equation:

(1/3)(9-x)-6=x

We move all terms to the left:

(1/3)(9-x)-6-(x)=0


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

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-1x^2+1/3*9)-1x-6=0

We multiply all the terms by the denominator


(-1x^2+1-1x*3*9)-6*3*9)=0

We add all the numbers together, and all the variables

(-1x^2+1-1x*3*9)=0

We get rid of parentheses

-1x^2-1x*3*9+1=0

Wy multiply elements

-1x^2-27x*9+1=0

Wy multiply elements

-1x^2-243x+1=0

a = -1; b = -243; c = +1;
Δ = b2-4ac
Δ = -2432-4·(-1)·1
Δ = 59053
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{-(-243)-\sqrt{59053}}{2*-1}=\frac{243-\sqrt{59053}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-243)+\sqrt{59053}}{2*-1}=\frac{243+\sqrt{59053}}{-2}
$