2/3x-9=2x+3

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

2/3x-9=2x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2-9x-27x+2=0

We add all the numbers together, and all the variables

-6x^2-36x+2=0

a = -6; b = -36; c = +2;
Δ = b2-4ac
Δ = -362-4·(-6)·2
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*-6}=\frac{36-8\sqrt{21}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*-6}=\frac{36+8\sqrt{21}}{-12}
$