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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+2/3x-11=0

We multiply all the terms by the denominator


-2x*3x-11*3x+2=0

Wy multiply elements

-6x^2-33x+2=0

a = -6; b = -33; c = +2;
Δ = b2-4ac
Δ = -332-4·(-6)·2
Δ = 1137
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{-(-33)-\sqrt{1137}}{2*-6}=\frac{33-\sqrt{1137}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1137}}{2*-6}=\frac{33+\sqrt{1137}}{-12}
$