40/x=20/3x-5

Solution for 40/x=20/3x-5 equation:

40/x=20/3x-5

We move all terms to the left:

40/x-(20/3x-5)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

40/x-20/3x+5=0

We calculate fractions


120x/3x^2+(-20x)/3x^2+5=0

We multiply all the terms by the denominator


120x+(-20x)+5*3x^2=0

Wy multiply elements

15x^2+120x+(-20x)=0

We get rid of parentheses

15x^2+120x-20x=0

We add all the numbers together, and all the variables

15x^2+100x=0

a = 15; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·15·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*15}=\frac{-200}{30}
=-6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*15}=\frac{0}{30}
=0
$