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

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

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

We move all terms to the left:

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


Domain of the equation: 3x-7))!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x*3x+2*3x-7))-((-6))=0

We add all the numbers together, and all the variables

x*3x+2*3x=0

Wy multiply elements

3x^2+6x=0

a = 3; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·3·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*3}=\frac{0}{6}
=0
$