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

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

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

We move all terms to the left:

-2/5x+3-(2/3x+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

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

We calculate fractions


(-6x)/15x^2+(-10x)/15x^2-2+3=0

We add all the numbers together, and all the variables

(-6x)/15x^2+(-10x)/15x^2+1=0

We multiply all the terms by the denominator


(-6x)+(-10x)+1*15x^2=0

Wy multiply elements

15x^2+(-6x)+(-10x)=0

We get rid of parentheses

15x^2-6x-10x=0

We add all the numbers together, and all the variables

15x^2-16x=0

a = 15; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·15·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*15}=\frac{32}{30}
=1+1/15
$