4/7x+1=3/x+2

Solution for 4/7x+1=3/x+2 equation:

4/7x+1=3/x+2

We move all terms to the left:

4/7x+1-(3/x+2)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



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

x∈R


We get rid of parentheses

4/7x-3/x-2+1=0

We calculate fractions


4x/7x^2+(-21x)/7x^2-2+1=0

We add all the numbers together, and all the variables

4x/7x^2+(-21x)/7x^2-1=0

We multiply all the terms by the denominator


4x+(-21x)-1*7x^2=0

Wy multiply elements

-7x^2+4x+(-21x)=0

We get rid of parentheses

-7x^2+4x-21x=0

We add all the numbers together, and all the variables

-7x^2-17x=0

a = -7; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-7)·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*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-7}=\frac{34}{-14}
=-2+3/7
$