3/5x+2=2/3x-4

Solution for 3/5x+2=2/3x-4 equation:

3/5x+2=2/3x-4

We move all terms to the left:

3/5x+2-(2/3x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

3/5x-2/3x+4+2=0

We calculate fractions


9x/15x^2+(-10x)/15x^2+4+2=0

We add all the numbers together, and all the variables

9x/15x^2+(-10x)/15x^2+6=0

We multiply all the terms by the denominator


9x+(-10x)+6*15x^2=0

Wy multiply elements

90x^2+9x+(-10x)=0

We get rid of parentheses

90x^2+9x-10x=0

We add all the numbers together, and all the variables

90x^2-1x=0

a = 90; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·90·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*90}=\frac{0}{180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*90}=\frac{2}{180}
=1/90
$