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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/15x^2+(-9x)/15x^2-4-5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-135x^2+10x+(-9x)=0

We get rid of parentheses

-135x^2+10x-9x=0

We add all the numbers together, and all the variables

-135x^2+x=0

a = -135; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-135)·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*-135}=\frac{-2}{-270}
=1/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-135}=\frac{0}{-270}
=0
$