2/x=12/7x-3

Solution for 2/x=12/7x-3 equation:

2/x=12/7x-3

We move all terms to the left:

2/x-(12/7x-3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x-3)!=0

x∈R


We get rid of parentheses

2/x-12/7x+3=0

We calculate fractions


14x/7x^2+(-12x)/7x^2+3=0

We multiply all the terms by the denominator


14x+(-12x)+3*7x^2=0

Wy multiply elements

21x^2+14x+(-12x)=0

We get rid of parentheses

21x^2+14x-12x=0

We add all the numbers together, and all the variables

21x^2+2x=0

a = 21; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·21·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*21}=\frac{-4}{42}
=-2/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*21}=\frac{0}{42}
=0
$