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

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

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

We move all terms to the left:

-4/5x+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

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

We calculate fractions


(-108x)/135x^2+10x/135x^2+20x/135x^2+1=0

We multiply all the terms by the denominator


(-108x)+10x+20x+1*135x^2=0

We add all the numbers together, and all the variables

30x+(-108x)+1*135x^2=0

Wy multiply elements

135x^2+30x+(-108x)=0

We get rid of parentheses

135x^2+30x-108x=0

We add all the numbers together, and all the variables

135x^2-78x=0

a = 135; b = -78; c = 0;
Δ = b2-4ac
Δ = -782-4·135·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-78}{2*135}=\frac{0}{270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+78}{2*135}=\frac{156}{270}
=26/45
$