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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x*3x+2*3x+7*3x-2=0

Wy multiply elements

3x^2+6x+21x-2=0

We add all the numbers together, and all the variables

3x^2+27x-2=0

a = 3; b = 27; c = -2;
Δ = b2-4ac
Δ = 272-4·3·(-2)
Δ = 753
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{-(27)-\sqrt{753}}{2*3}=\frac{-27-\sqrt{753}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{753}}{2*3}=\frac{-27+\sqrt{753}}{6}
$