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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-3x^2)/6x^2+14x/6x^2-1-1=0

We add all the numbers together, and all the variables

(-3x^2)/6x^2+14x/6x^2-2=0

We multiply all the terms by the denominator


(-3x^2)+14x-2*6x^2=0

Wy multiply elements

(-3x^2)-12x^2+14x=0

We get rid of parentheses

-3x^2-12x^2+14x=0

We add all the numbers together, and all the variables

-15x^2+14x=0

a = -15; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-15)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-15}=\frac{-28}{-30}
=14/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-15}=\frac{0}{-30}
=0
$