5/3x-4/5x-1=8

Solution for 5/3x-4/5x-1=8 equation:

5/3x-4/5x-1=8

We move all terms to the left:

5/3x-4/5x-1-(8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-4/5x-9=0

We calculate fractions


25x/15x^2+(-12x)/15x^2-9=0

We multiply all the terms by the denominator


25x+(-12x)-9*15x^2=0

Wy multiply elements

-135x^2+25x+(-12x)=0

We get rid of parentheses

-135x^2+25x-12x=0

We add all the numbers together, and all the variables

-135x^2+13x=0

a = -135; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-135)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-135}=\frac{-26}{-270}
=13/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-135}=\frac{0}{-270}
=0
$