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

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

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

We move all terms to the left:

-8/3x-8-(-8/5x-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

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

We calculate fractions


(-40x)/15x^2+24x/15x^2+2-8=0

We add all the numbers together, and all the variables

(-40x)/15x^2+24x/15x^2-6=0

We multiply all the terms by the denominator


(-40x)+24x-6*15x^2=0

We add all the numbers together, and all the variables

24x+(-40x)-6*15x^2=0

Wy multiply elements

-90x^2+24x+(-40x)=0

We get rid of parentheses

-90x^2+24x-40x=0

We add all the numbers together, and all the variables

-90x^2-16x=0

a = -90; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-90)·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*-90}=\frac{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-90}=\frac{32}{-180}
=-8/45
$