2/3x-2=7/6x+20

Solution for 2/3x-2=7/6x+20 equation:

2/3x-2=7/6x+20

We move all terms to the left:

2/3x-2-(7/6x+20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+20)!=0

x∈R


We get rid of parentheses

2/3x-7/6x-20-2=0

We calculate fractions


12x/18x^2+(-21x)/18x^2-20-2=0

We add all the numbers together, and all the variables

12x/18x^2+(-21x)/18x^2-22=0

We multiply all the terms by the denominator


12x+(-21x)-22*18x^2=0

Wy multiply elements

-396x^2+12x+(-21x)=0

We get rid of parentheses

-396x^2+12x-21x=0

We add all the numbers together, and all the variables

-396x^2-9x=0

a = -396; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-396)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-396}=\frac{0}{-792}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-396}=\frac{18}{-792}
=-1/44
$