2x-1/5=3/10(x-1)+0,2

Solution for 2x-1/5=3/10(x-1)+0,2 equation:

2x-1/5=3/10(x-1)+0.2

We move all terms to the left:

2x-1/5-(3/10(x-1)+0.2)=0


Domain of the equation: 10(x-1)+0.2)!=0

x∈R


We calculate fractions


2x+()/(10x-10)+(-10xx/(10x-10)=0


We calculate terms in parentheses: +(-10xx/(10x-10), so:

-10xx/(10x-10

We multiply all the terms by the denominator


-10xx

Back to the equation:

+(-10xx)


We get rid of parentheses

2x+()/(10x-10)-10xx=0

We multiply all the terms by the denominator


2x*(10x-10)-10xx*(10x-10)+()=0

We add all the numbers together, and all the variables

2x*(10x-10)-10xx*(10x-10)=0

We multiply parentheses

20x^2-100x^2-20x+100x=0

We add all the numbers together, and all the variables

-80x^2+80x=0

a = -80; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-80)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-80}=\frac{-160}{-160}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-80}=\frac{0}{-160}
=0
$