-2/x+3/5x=20

Solution for -2/x+3/5x=20 equation:

-2/x+3/5x=20

We move all terms to the left:

-2/x+3/5x-(20)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


(-10x)/5x^2+3x/5x^2-20=0

We multiply all the terms by the denominator


(-10x)+3x-20*5x^2=0

We add all the numbers together, and all the variables

3x+(-10x)-20*5x^2=0

Wy multiply elements

-100x^2+3x+(-10x)=0

We get rid of parentheses

-100x^2+3x-10x=0

We add all the numbers together, and all the variables

-100x^2-7x=0

a = -100; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-100)·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*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-100}=\frac{14}{-200}
=-7/100
$