-1/7x-2=2/3x+3

Solution for -1/7x-2=2/3x+3 equation:

-1/7x-2=2/3x+3

We move all terms to the left:

-1/7x-2-(2/3x+3)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

-1/7x-2/3x-3-2=0

We calculate fractions


(-3x)/21x^2+(-14x)/21x^2-3-2=0

We add all the numbers together, and all the variables

(-3x)/21x^2+(-14x)/21x^2-5=0

We multiply all the terms by the denominator


(-3x)+(-14x)-5*21x^2=0

Wy multiply elements

-105x^2+(-3x)+(-14x)=0

We get rid of parentheses

-105x^2-3x-14x=0

We add all the numbers together, and all the variables

-105x^2-17x=0

a = -105; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-105)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-105}=\frac{0}{-210}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-105}=\frac{34}{-210}
=-17/105
$