2/3x-9-12/3-x=1

Solution for 2/3x-9-12/3-x=1 equation:

2/3x-9-12/3-x=1

We move all terms to the left:

2/3x-9-12/3-x-(1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


determiningTheFunctionDomain
2/3x-x-9-1-12/3=0

We add all the numbers together, and all the variables

-1x+2/3x-14=0

We multiply all the terms by the denominator


-1x*3x-14*3x+2=0

Wy multiply elements

-3x^2-42x+2=0

a = -3; b = -42; c = +2;
Δ = b2-4ac
Δ = -422-4·(-3)·2
Δ = 1788
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1788}=\sqrt{4*447}=\sqrt{4}*\sqrt{447}=2\sqrt{447}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{447}}{2*-3}=\frac{42-2\sqrt{447}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{447}}{2*-3}=\frac{42+2\sqrt{447}}{-6}
$