-5/3x+1/3=4/5x+13

Solution for -5/3x+1/3=4/5x+13 equation:

-5/3x+1/3=4/5x+13

We move all terms to the left:

-5/3x+1/3-(4/5x+13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+13)!=0

x∈R


We get rid of parentheses

-5/3x-4/5x-13+1/3=0

We calculate fractions


(-25x)/135x^2+(-108x)/135x^2+5x/135x^2-13=0

We multiply all the terms by the denominator


(-25x)+(-108x)+5x-13*135x^2=0

We add all the numbers together, and all the variables

5x+(-25x)+(-108x)-13*135x^2=0

Wy multiply elements

-1755x^2+5x+(-25x)+(-108x)=0

We get rid of parentheses

-1755x^2+5x-25x-108x=0

We add all the numbers together, and all the variables

-1755x^2-128x=0

a = -1755; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·(-1755)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*-1755}=\frac{0}{-3510}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*-1755}=\frac{256}{-3510}
=-128/1755
$