3/x=5/3x-10

Solution for 3/x=5/3x-10 equation:

3/x=5/3x-10

We move all terms to the left:

3/x-(5/3x-10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-10)!=0

x∈R


We get rid of parentheses

3/x-5/3x+10=0

We calculate fractions


9x/3x^2+(-5x)/3x^2+10=0

We multiply all the terms by the denominator


9x+(-5x)+10*3x^2=0

Wy multiply elements

30x^2+9x+(-5x)=0

We get rid of parentheses

30x^2+9x-5x=0

We add all the numbers together, and all the variables

30x^2+4x=0

a = 30; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·30·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*30}=\frac{-8}{60}
=-2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*30}=\frac{0}{60}
=0
$