1/5x-4/3=2/3x+1

Solution for 1/5x-4/3=2/3x+1 equation:

1/5x-4/3=2/3x+1

We move all terms to the left:

1/5x-4/3-(2/3x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

1/5x-2/3x-1-4/3=0

We calculate fractions


27x/135x^2+(-10x)/135x^2+(-20x)/135x^2-1=0

We multiply all the terms by the denominator


27x+(-10x)+(-20x)-1*135x^2=0

Wy multiply elements

-135x^2+27x+(-10x)+(-20x)=0

We get rid of parentheses

-135x^2+27x-10x-20x=0

We add all the numbers together, and all the variables

-135x^2-3x=0

a = -135; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-135)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-135}=\frac{0}{-270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-135}=\frac{6}{-270}
=-1/45
$