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

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

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

We move all terms to the left:

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

We calculate fractions


125x/375x^2+(-3x)/375x^2+9x/375x^2-2=0

We multiply all the terms by the denominator


125x+(-3x)+9x-2*375x^2=0

We add all the numbers together, and all the variables

134x+(-3x)-2*375x^2=0

Wy multiply elements

-750x^2+134x+(-3x)=0

We get rid of parentheses

-750x^2+134x-3x=0

We add all the numbers together, and all the variables

-750x^2+131x=0

a = -750; b = 131; c = 0;
Δ = b2-4ac
Δ = 1312-4·(-750)·0
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(131)-131}{2*-750}=\frac{-262}{-1500}
=131/750
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(131)+131}{2*-750}=\frac{0}{-1500}
=0
$