3/x-4=2/7x

Solution for 3/x-4=2/7x equation:

3/x-4=2/7x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-28x^2+21x+(-2x)=0

We get rid of parentheses

-28x^2+21x-2x=0

We add all the numbers together, and all the variables

-28x^2+19x=0

a = -28; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-28)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-28}=\frac{-38}{-56}
=19/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-28}=\frac{0}{-56}
=0
$