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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-40x)/50x^2+(-10x)/50x^2+4+1=0

We add all the numbers together, and all the variables

(-40x)/50x^2+(-10x)/50x^2+5=0

We multiply all the terms by the denominator


(-40x)+(-10x)+5*50x^2=0

Wy multiply elements

250x^2+(-40x)+(-10x)=0

We get rid of parentheses

250x^2-40x-10x=0

We add all the numbers together, and all the variables

250x^2-50x=0

a = 250; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·250·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*250}=\frac{0}{500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*250}=\frac{100}{500}
=1/5
$