2/10x-4/10x=1/5x-1

Solution for 2/10x-4/10x=1/5x-1 equation:

2/10x-4/10x=1/5x-1

We move all terms to the left:

2/10x-4/10x-(1/5x-1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

2/10x-4/10x-1/5x+1=0

We calculate fractions


(-20x+2)/50x^2+(-10x)/50x^2+1=0

We multiply all the terms by the denominator


(-20x+2)+(-10x)+1*50x^2=0

Wy multiply elements

50x^2+(-20x+2)+(-10x)=0

We get rid of parentheses

50x^2-20x-10x+2=0

We add all the numbers together, and all the variables

50x^2-30x+2=0

a = 50; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·50·2
Δ = 500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{5}}{2*50}=\frac{30-10\sqrt{5}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{5}}{2*50}=\frac{30+10\sqrt{5}}{100}
$