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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

37x+(-10x)-2*135x^2=0

Wy multiply elements

-270x^2+37x+(-10x)=0

We get rid of parentheses

-270x^2+37x-10x=0

We add all the numbers together, and all the variables

-270x^2+27x=0

a = -270; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-270)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-270}=\frac{-54}{-540}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-270}=\frac{0}{-540}
=0
$