-2/3x-8=3/5x-4

Solution for -2/3x-8=3/5x-4 equation:

-2/3x-8=3/5x-4

We move all terms to the left:

-2/3x-8-(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+4-8=0

We calculate fractions


(-10x)/15x^2+(-9x)/15x^2+4-8=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-60x^2+(-10x)+(-9x)=0

We get rid of parentheses

-60x^2-10x-9x=0

We add all the numbers together, and all the variables

-60x^2-19x=0

a = -60; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-60)·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*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-60}=\frac{38}{-120}
=-19/60
$