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

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



(1/3)(9-6x)=x
We move all terms to the left:
(1/3)(9-6x)-(x)=0
Domain of the equation: 3)(9-6x)!=0
x∈R
We add all the numbers together, and all the variables
(+1/3)(-6x+9)-x=0
We add all the numbers together, and all the variables
-1x+(+1/3)(-6x+9)=0
We multiply parentheses ..
(-6x^2+1/3*9)-1x=0
We multiply all the terms by the denominator
(-6x^2+1-1x*3*9)=0
We get rid of parentheses
-6x^2-1x*3*9+1=0
Wy multiply elements
-6x^2-27x*9+1=0
Wy multiply elements
-6x^2-243x+1=0
a = -6; b = -243; c = +1;
Δ = b2-4ac
Δ = -2432-4·(-6)·1
Δ = 59073
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{59073}}{2*-6}=\frac{243-\sqrt{59073}}{-12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-243)+\sqrt{59073}}{2*-6}=\frac{243+\sqrt{59073}}{-12} $

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