-5/3x-4=4/4x-5

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

-5/3x-4=4/4x-5

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-20x)/12x^2+(-12x)/12x^2+5-4=0

We add all the numbers together, and all the variables

(-20x)/12x^2+(-12x)/12x^2+1=0

We multiply all the terms by the denominator


(-20x)+(-12x)+1*12x^2=0

Wy multiply elements

12x^2+(-20x)+(-12x)=0

We get rid of parentheses

12x^2-20x-12x=0

We add all the numbers together, and all the variables

12x^2-32x=0

a = 12; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·12·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*12}=\frac{64}{24}
=2+2/3
$