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

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

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

We move all terms to the left:

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

We calculate fractions


3x/375x^2+(-250x)/375x^2+6x/375x^2-2=0

We multiply all the terms by the denominator


3x+(-250x)+6x-2*375x^2=0

We add all the numbers together, and all the variables

9x+(-250x)-2*375x^2=0

Wy multiply elements

-750x^2+9x+(-250x)=0

We get rid of parentheses

-750x^2+9x-250x=0

We add all the numbers together, and all the variables

-750x^2-241x=0

a = -750; b = -241; c = 0;
Δ = b2-4ac
Δ = -2412-4·(-750)·0
Δ = 58081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{58081}=241$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-241)-241}{2*-750}=\frac{0}{-1500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-241)+241}{2*-750}=\frac{482}{-1500}
=-241/750
$