2/x=3/5x-7

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

2/x=3/5x-7

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/5x^2+(-3x)/5x^2+7=0

We multiply all the terms by the denominator


10x+(-3x)+7*5x^2=0

Wy multiply elements

35x^2+10x+(-3x)=0

We get rid of parentheses

35x^2+10x-3x=0

We add all the numbers together, and all the variables

35x^2+7x=0

a = 35; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·35·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*35}=\frac{-14}{70}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*35}=\frac{0}{70}
=0
$