2/3x+3/5=5/15x-3

Solution for 2/3x+3/5=5/15x-3 equation:

2/3x+3/5=5/15x-3

We move all terms to the left:

2/3x+3/5-(5/15x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x-3)!=0

x∈R


We get rid of parentheses

2/3x-5/15x+3+3/5=0

We calculate fractions


135x^2/1125x^2+750x/1125x^2+(-375x)/1125x^2+3=0

We multiply all the terms by the denominator


135x^2+750x+(-375x)+3*1125x^2=0

Wy multiply elements

135x^2+3375x^2+750x+(-375x)=0

We get rid of parentheses

135x^2+3375x^2+750x-375x=0

We add all the numbers together, and all the variables

3510x^2+375x=0

a = 3510; b = 375; c = 0;
Δ = b2-4ac
Δ = 3752-4·3510·0
Δ = 140625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{140625}=375$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(375)-375}{2*3510}=\frac{-750}{7020}
=-25/234
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(375)+375}{2*3510}=\frac{0}{7020}
=0
$