2/x=7/3x-5

Solution for 2/x=7/3x-5 equation:

2/x=7/3x-5

We move all terms to the left:

2/x-(7/3x-5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

2/x-7/3x+5=0

We calculate fractions


6x/3x^2+(-7x)/3x^2+5=0

We multiply all the terms by the denominator


6x+(-7x)+5*3x^2=0

Wy multiply elements

15x^2+6x+(-7x)=0

We get rid of parentheses

15x^2+6x-7x=0

We add all the numbers together, and all the variables

15x^2-1x=0

a = 15; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·15·0
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*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*15}=\frac{2}{30}
=1/15
$