5-1/3x=3/5x-2

Solution for 5-1/3x=3/5x-2 equation:

5-1/3x=3/5x-2

We move all terms to the left:

5-1/3x-(3/5x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-2)!=0

x∈R


We get rid of parentheses

-1/3x-3/5x+2+5=0

We calculate fractions


(-5x)/15x^2+(-9x)/15x^2+2+5=0

We add all the numbers together, and all the variables

(-5x)/15x^2+(-9x)/15x^2+7=0

We multiply all the terms by the denominator


(-5x)+(-9x)+7*15x^2=0

Wy multiply elements

105x^2+(-5x)+(-9x)=0

We get rid of parentheses

105x^2-5x-9x=0

We add all the numbers together, and all the variables

105x^2-14x=0

a = 105; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·105·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*105}=\frac{0}{210}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*105}=\frac{28}{210}
=2/15
$