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

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

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

We move all terms to the left:

2/3x-3-(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

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

We calculate fractions


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

We add all the numbers together, and all the variables

10x/15x^2+(-3x)/15x^2-5=0

We multiply all the terms by the denominator


10x+(-3x)-5*15x^2=0

Wy multiply elements

-75x^2+10x+(-3x)=0

We get rid of parentheses

-75x^2+10x-3x=0

We add all the numbers together, and all the variables

-75x^2+7x=0

a = -75; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-75)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-75}=\frac{-14}{-150}
=7/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-75}=\frac{0}{-150}
=0
$