60/5x-3=40/3x+2

Solution for 60/5x-3=40/3x+2 equation:

60/5x-3=40/3x+2

We move all terms to the left:

60/5x-3-(40/3x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

60/5x-40/3x-2-3=0

We calculate fractions


180x/15x^2+(-200x)/15x^2-2-3=0

We add all the numbers together, and all the variables

180x/15x^2+(-200x)/15x^2-5=0

We multiply all the terms by the denominator


180x+(-200x)-5*15x^2=0

Wy multiply elements

-75x^2+180x+(-200x)=0

We get rid of parentheses

-75x^2+180x-200x=0

We add all the numbers together, and all the variables

-75x^2-20x=0

a = -75; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-75)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-75}=\frac{0}{-150}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-75}=\frac{40}{-150}
=-4/15
$