2/3x-8=9-3/5x

Solution for 2/3x-8=9-3/5x equation:

2/3x-8=9-3/5x

We move all terms to the left:

2/3x-8-(9-3/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-3/5x+9)-8=0

We get rid of parentheses

2/3x+3/5x-9-8=0

We calculate fractions


10x/15x^2+9x/15x^2-9-8=0

We add all the numbers together, and all the variables

10x/15x^2+9x/15x^2-17=0

We multiply all the terms by the denominator


10x+9x-17*15x^2=0

We add all the numbers together, and all the variables

19x-17*15x^2=0

Wy multiply elements

-255x^2+19x=0

a = -255; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-255)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-255}=\frac{-38}{-510}
=19/255
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-255}=\frac{0}{-510}
=0
$