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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


7x/3x^2+(-6x)/3x^2-2+1=0

We add all the numbers together, and all the variables

7x/3x^2+(-6x)/3x^2-1=0

We multiply all the terms by the denominator


7x+(-6x)-1*3x^2=0

Wy multiply elements

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

We get rid of parentheses

-3x^2+7x-6x=0

We add all the numbers together, and all the variables

-3x^2+x=0

a = -3; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-3)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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